I'm describing earlier-game than this - with Monarchy you can harvest Wine, and are usually close to or already have Calendar. Unhappiness kicks in at 4-5 pop, and cities grow past this stage very quickly. The only realistic way to control happiness without religion this early is Construction (colosseum), which forces a suboptimal tech route at that stage in the game (precisely because it delays Monarchy, Alphabet and Calendar).
Later still. 'Early game' = Ancient/Classical Era, at most early Medieval.
Sorry but the above is absolute nonsense....For starters both Drama and Monarchy are classical techs....
Monarchy allows Hereditary Rule allowing for potentially unlimited happiness, wine is nothing more than a small bonus. It also costs significantly less

to research all of Meditation, Priesthood, Mysticism and Monarchy combined than it does to research just Maths and Construction or Maths and Calender.
Drama+Aesthetics costs just a tiny bit more than Maths+Construction (just 10

on Emperor difficulty), provides vastly more happiness potential (2 per 10% of the culture slider with a Theatre, 1 without) and at a very low cost (Theatres cost just 50

a piece).
Compare those to Construction, which offers just 1 happiness from a Colliseum for 80

, its a building that is rarely worth building until much later in the game, if at all....
or Calender which is only worth getting early if you have most of its resources, or are forced to settle jungle with resources early, requires Iron Working to be worth having at all AND requires an army of workers to clear the jungle and improve those resources.
True, but also only really a factor once you have resources to connect to your trade network.
Why? Each new city starts with the 4 or so starting

allowing you to grow that much extra pop, and each new city will also benefit from any resources or bonuses you have, and can build extra copies of buildings, of particular note early with small cities are

producing ones and ones that allow specialsits (Libraires).
Obviously you need to start growing your cities eventually, but Monarchy is easy to get early.
Useful, but at this stage in the game I'm also often struggling to find useful things to spend hammers on in any case, due the below-mentioned nature of the early-game tech paths, and the religious restriction on several early-game buildings such as temples and monasteries. After Granary, Library and Barracks, without religion you tend to be short of things to do until you hit Currency and the subsequent techs; even Wonders, the usual hammer-sink in Civ games, are fairly sparsely scattered through the early tech tree. I prefer not to invest in Walls and Aqueducts just because there's nothing better to do, and Barracks for the most part - even Libraries in cities without commerce (not that I usually have many of those, plus Libraries are better than Monuments as an early culture building).
You could build more units, either for war or happiness under HR. Or more workers/settlers for expansion. With alphabet you can also build research directly (obviously this can't be whipped), which is a good hammer sink until Wealth with Currency. You already mentioned wonders too.
Also, Libraries are not only good in cities with high commerce, cities with good food output are also good sites that allow you to run scientists
and on that note the other method I forgot to mention was to run specialists, most likely scientists in cities to keep pop low while making cities very productive.
My traditional tech route is indeed to go to Code of Laws. The fact that such 'poor play' tech paths exist at all feeds into one of my points below. Also, these techs tend to be heavily-dependent on the religion they provide for their benefits - for instance, if you don't get Buddhism there is essentially no reason to get Meditation except as a 'bridging tech' to the more useful techs it enables. Monuments make Polytheism marginally more useful.
Med doesn't just allow a Monastery of buddhism, it allows one of any religion you have in your cities. Obviously that isn't helpful in isolation, but would you bother making Optics a priority in civ 5 on an inland start

?
The problem is that you gain too little benefit from growing cities very far (since before you reach that stage you'll be working all workable tiles, and probably have a couple of specialists to boot) at that stage in the game - so even if the health penalty kicks in, unless it actively leads to starvation it's irrrelevant. Slow growth is if anything beneficial.
One of your previous posts suggests to me you leave a lotof forests lying around, in which case having excess

is very likely, but comes at the expense of a lot of early production and useable tiles as forests are very weak to work till Replaceable Parts.
If you use up the forests to get a strong start you can start hitting the health cap in the midgame forcing a lot of trade, and industrialisation does cause problems.
Theres no actual benefit in slow growth, more pop means more output and more score, and is worth it provided you have enough happiness, which is usually abundant by this point. Without the health cap sid's sushi would run riot over everything in the late game.
I'd say it's the very early game stages, when nothing costs much, you don't have much income, and 1-2 extra production or commerce can make a turn's difference in unit/structure completion or research completion, that working unimproved tiles has value.
Growing onto an unimproved tile while building a Worker would only slow the construction of the Worker you are building....and the returns on that worker will speed up everything that follows except maybe the next build under certain circumstance, most will be faster, especially if you consdier chopping, but there may be one or two ways a worker will slow it perhaps.
An extra commerce or two is only going to make a difference if your looking to found the earliest religions.... and if you really want to do that then theres little point in building a worker as you likely won't have the techs needed to improve tiles.
The issue isn't so much that there aren't a few viable alternatives to choose from - it's that these are scattered amid choices that are *always* suboptimal (such as the your own example of the Hinduism/Buddhism path); the actual viable options are limited and tend to branch out later in the tech tree (when a player might already have made the wrong early calls and be set behind). My feeling is that in better game designs, every option should have an appropriate use in the right circumstances; options should exist only insofar as they add strategic utility, rather than being there in part to obfuscate the correct tech choices. It's much like the option in chess to turn a pawn into a bishop or rook instead of a queen - there's never any point to it, to the extent that players are often unaware that it's actually possible to turn the pawn into anything other than a queen. Meditation, for instance, shouldn't be where it is on the tech tree - the monastery is only useful with a religion, and you'll never get Buddhism before the AI above Warlord. There's no logical reason for it to be a requirement for Code of Laws, and indeed no (game, as opposed to thematic) purpose in linking the monastery to Meditation rather than any other tech you need to unlock before reaching Confucianism.
Well people have shown that early religion founding can work even on Diety, though to get enough benefit to justify the risk requires a player to
really know what they are doing with it.