Umm... OP said he wants to stay in HR to grow cities big and run specialists. This was exactly the example to show why this is not worth it.
As for your example, I pretty much never build cottages outside capital, except maybe if I'm financial. Growing cottages is too much of a drain on early expansion and conquest. The first 30 turns a cottage is only as good or worse than a grassland farm, and grassland farms I rather whip out than keep working. Spending 30 turns early on working a tile I'd rather whip out is not my thing.
In the late game there are other improvements available that are just as good or better than towns. By the time you get to the industrial era, if the empire is well managed, you should be able to keep slider at 100% by building wealth/failgold/selling techs and so on, and still have hammers to spare to build research. Since hammers are turned into beakers, one hammer equals one beaker at this point. I usually prefer State Property and workshops. A town is +5

while a SP workshop is +4

. When you factor in multipliers, pretty much all your cities will have +110% hammers with forge, factory, power and SP. That turns 4 hammers into 8.8

. A town comes out slightly ahead at 9.25

, if we assume library, uni, observatory and Free Religion. But Free Religion is often a worse option than Pacifism and getting up uni and observatory while working cottages is a long and tedious process. In contrast, getting up factories and power plants with workshops is lightning fast. And the hammers are also more versatile as they can be used for hammers as well, if needed. For the cottages to come out ahead, you need Free Speech or at least US.
And let's not forget about SP watermills, which are even stronger than workshops.
However, the main difference comes with faster expansion. I'm currently in the industrial era in a space game and if I exclude capital, the remaining active cities make an average of 100

/city, which will still rise as many are still getting up power plants and other infra. Most cities are equally improved to work max hammers with some rep scientists. If I slowed down early expansion to work cottages, I would have less cities. Having a few towns to replace workshops for a very marginal benefit could not possibly make up for the loss of even having 1 or 2 less cities at this stage of the game.