I've updated the card to deal with some of the issues
1) There's no switching phases, and you can at least play villages now. You can basically only play 1 terminal (excluding villagers, coin of the realm, throne room variants, or other shtick).
2) The fact that your extra turn is weakened is not as big as you're making it out to be. Outpost and Mission also have restrictions because extra turns are a big deal (If i can double province each turn, getting an extra turn unconditionally would be like a card that gave you 2 provinces). I could say that I would never buy outposts in big money and I would only buy it in engines with great trashing (or with guide or minion); that's the point! It's not always supposed to be a viable card, it depends on the board. It's also supposed to make your extra turn harder, or else getting the extra turn would be a no-brainer (extra turns are powerful, especially at the end). Mission costs $4 for a single extra turn that you can't buy cards. What's the point of having an extra turn if you can't buy cards? Plenty if you're creative enough; you can trash cards, cycle through your deck, upgrade travellers, gain coffers, gain villagers, gain victory tokens, or gain cards. You might not buy it with big money, or with an engine that can't do much of those things above, but you will buy it in the cases where it is helpful. In this case you get an extra turn where you can only play one terminal. Is that worth it? depends on what your non-terminals can do. I think there's plenty of situations where I would buy a Grand Tour at it's price point (especially since you only buy one of them).
3) There are plenty of engines that could run without villages; scrying pool, throne room variants, villagers, coin of the realm, labs/alchemists, Cantrip decks (like Grand Market), single card engines (minion or governor). Also, like you said this would work with big money.
4) I'm thinking the price would have problems if $4 or less. Opening with it would be very powerful, since in the beginning, nobody has too many terminals and extra turns in the beginning are great when you're trying to build your deck. Then, if you don't need it you could trash it or leave it in your deck if you have to.