I will say that some legacy paths work well. The antiquity ones, the enlightenment one, and space race are all things you want to be doing anyway when playing an ordinary Civ game. They don't really roadblock as much
For me the problematic ones are the ones which effectively create a minigame. Relics/archaeology, railroads/treasure fleets... These are what you have to do to win the game and yet are a bit of a departure from how you would play normally... I guess this is shining the light on culture always being a minigame in other civ versions too but it's annoying when the culture and economic paths start off really fun.
The millitary ones add hoops onto something you'd already do too so it's not so bad... But the roadblocks are odd. For me they are in the middle.
I have two basic problems with the Legacy Paths in the game right now. The first is that too many of the Legacy Paths involve virtually no conflict or strife with any other element in the game other than your own priorities.
Examples:
Antiquity Science Path requires you to display Codexes in your settlements (cities). But you get most if not all of the Codexes from the Civics Tree, and short of completely conquering and eliminating you, there is nothing any other player can do to stop you from 'researching' enough Civics. The only 'conflict' is whether you want to build Markets and Lighthouses to use Resources before or after you build Libraries and Academies to display the Codexes - and whether you have enough cities (two, each with a Library and an Academy are enough to complete the Path) left.
Exploration Culture Path requires you to get and display Relics - this time in Temples primarily. But again, with the right Pantheon you can get 2 Relics every time you convert an opposing Capital for the first time. Unless you are playing a Duel game with only one opponent, 2 - 3 Missionaries will convert enough capitals to give you all the Relics you need - and it doesn't even matter if every one of the Capitals gets converted back later. Nor is there, as far as I can see, any mechanic in the game that affects Missionaries - they can trot right through armies, fleets, erupting volcanoes, nuclear weapons - build them and convert, later build a few Temples and the Path is done regardless of what anybody or anything else in the game does. I generally complete the path within 30 - 40 Turns anymore.
Similarly, the Exploration Science Path requires you to build up 5 Urban areas to 40+ adjacency/bonus points. Again, short of conquering the cities with those districts in them from you, there is nothing anybody else can do to stop you from getting them once you know enough about adjacencies in cities.
Finding Treasure resources, building Settlements and trading enough Resources to complete the Exploration Economic Path, or building enough railroads and Factories to complete the Modern Economic Path are both time-consuming but sort of related to what you should be doing in each Age, as you said.
The Treasure Fleet/Economic Path also suffers from my second Major Gripe with the game.
Which is that all of the Legacies are utterly Linear and therefore contribute to playing the game the same way every time. If the game is based on Narrative History, then they recognize only one narrative and more or less force you to retell that narrative every single time.
So, in Antiquity you gather Codexes, gather Resources, conquer AI Civ settlements, build Wonders. Each is connected to a single Legacy Path, and is the Only Way to complete that path. IPs and City States, Diplomacy, Exploration are all merely means to other ends and have no direct effect on any Legacy. Note that there are no Wonders related to Trade or Economics, and no matter how many City States you have under your belt, In No Age do they contribute directly to any Path.
And the Linear Nature of all the Paths contributes to play of the game being a series of random shots. Get a lousy map, and the Treasure Fleets are impossible (as in, No Resources on any land mass within range or all resources hidden inland behind other Civ's settlements, both of which have happened to me and others more than once). Since you don't know the configuration of the Distant Lands in Antiquity, that means you play the entire Antiquity Age and then, no matter how well you completed the Economic Legacy Path in Antiquity, discover that the map prevents you from completing the Economic path in Exploration regardless of what you do - basically, you are playing Brandenburg-Prussia in EUIV, where trying to get a colony in South America or the Caribbean as Brandenburg is an exercise in futility comparable to trying to complete Civ VII's Economic Legacy Path when the nearest Treasure resource is 20 tiles away and requires you to conquer at least one settlement from the AI before you can even start your first Treasure Fleet. Fergetaboudit.
As a result of the disconnect between in-game events and paths and the linear nature of the paths, Civ VII is already getting boring after 400 hours of play. In contrast, I played over 7000 hours of Civ V and 4500 hours of Civ VI without getting bored. This kind of 'progression does not bode well for the Civ VII game or the franchise.