Problem is, that breaks down completely when you go to multiplayer;
The separate strategic and action parts (where you can do each for as long as you want independently of the other without ill consequences in the neglected side), but where the strategic and action side enrich one another if you choose to play both of them, is one of my and Keith's core design goals for the game. I really don't think there's any way that auto-incrementing strategic turns would ever fit with that, or with multiplayer. Part of the reason for no auto-incrementing turns is that this isn't an RTS game, it's a TBS game. Having time pressure to do something before something else happens is absolutely counter to where I'd want to take this.
You're right that making it so that only having it auto-increment when you go back to settlements would handle most of those complaints, except multiplayer would be badly broken by that, but even in solo play that would lead to some undesirable consequences. Having to avoid town when you're low on supplies or just need to craft something new, because there's something bad that will happen when the turn auto-increments, creates a really unpleasant situation and I think that would be extremely common.
I hear what you're saying. My issue is that I don't see (in the current iteration) much synergy between the action and strategy parts. I think that a blend of genres needs to be justified in the sense that it needs to be more than the sum of its parts. Otherwise, separate the blend into 2 games where each could be better on its own. For example, the turn-based strategy in the game isn't really turn based. In a turn based game, the turns are your minimal time unit. So when a monster is next to a town, you better have some strategy to deal with that in the turn based realm because there's nothing else. The tension builds up over turns for that very reason. But in the current version, when a monster approaches the town, you have infinite chances outside of the turn-based space to eliminate said monster. Reacting to said monster is equivalent to a chore.
I really like the connection you made between exploration and the turn based game, since that connects the 2 parts in a way that enriches both: if I want to explore further, I need to move ahead in the turn-based game. The turn-based game gets a reason for you to play it (finish turns) and face the consequences of playing it (monsters, attacks, resource usage etc) and the action part gets new, interesting challenges as a result. However, if there's no feedback ie. if there's nothing within the action realm that will cause the turn-based game to advance, then all the turn-based game is doing is setting up static situations for the action parts to deal with. Within the action part, you can try as many times as you want to defeat the challenges set up in the turn-based part. The turn-based part then loses all tension, and the action part becomes a repeated loop.
I think it makes a lot of sense that going to craft stuff or heal fully will start a new turn. You're getting something you need, so there's a cost involved in terms of time. You can think of it as making the turn-based game more realtime, or alternatively, as putting the action into the turn-based realm. Each 'turn' then involves an expedition out into the world. More importantly, it makes the turn-based game relevant and intertwined with the choices of the player. Rather than seeing it as unpleasant, I see it as creating choices.
I think the critical point here is that it shouldn't be unpleasant because once the turn-based game becomes relevant, you're not going to try to fight a bunch of approaching monsters when they're right next to the town. That's something you'd never do in a turn based game because you'd know that you're not leaving yourself enough strategic depth to deal with the monsters in case you lose. It is something that's currently done in the game though, because the strategy isn't very relevant. What you'd do instead is go out there and try to nip it in the bud as early as you can (or as is reasonable) knowing that you need to leave yourself room to go back to town and heal perhaps several times, which could take a couple of turns.
I'm not sure what the plans for multiplayer are, but there are probably ways to translate this dynamic into multiplayer. For example, you could make it such that a turn advances every X visits to the towns, where X is the number of players. Alternatively, you could have it be such that if one player visits the town, all other players can have a chance to access the town's resources via that one player. It simplifies the alternative, which is one player taking gems from other players, then going to a town to craft it for them, and finally delivering the results to those players. Instead, each player gets a direct instant link to spell crafting.
BTW another idea (in general) is to enable you to visit each town once per turn. This creates a big incentive to find more towns.