The logistical logjams created by the stacking cap would certainly go away if that was implemented, and you could then add back useful things like worker stacks building single improvements faster. I like it.
Longer term I like the option to transition from the strategic map to a tactical one to fight battles (with stacks on the strategic scale) - with an autoresolve option for the big picture folks. I suspect that would be a Civ 6 sort of thing, but it's worth planting the seed.
While I think that's not a bad option, I'm with swornabsent - I think much of your original premise is incorrect. Many of the problems that you attribute to 1UPT aren't faults of the system, but faults of the AI and/or programming. Let's take those points 1 by 1.
1) It makes the mechanics of moving clunky and the game run very slow
True, but this isn't a fault of the system. This is a programming issue.
2) Roads are not only rare by design (fine) but almost useless in practice because of the stacking limit. Single NPC units can perma-block roads in neutral territory, and frequently do.
Absolutely and thank goodness. Throughout history there are countless tales of battles won and lost because of logistics. I think that moving your army to the battlefield is a skill and things do get delayed when you try to move a massive army at once.
In one of my Civ games, I was able to use an isolated unit to occupy a neutral road to slow down an advance on a favored City-State without declaring war. This gave the City-State more time to prepare (and a couple more turns to get a couple of my units in their territory to gift them to help with the defense). I love having those kinds of options. Where you see a problem, I see an opportunity to use that gameplay mechanic that I can use to my advantage.
3) It distorts the rest of the game
I think I understand what you're saying here, but you're implying causation without any proof whatsoever. Furthermore, I don't find the peace game boring except due to the lack of good diplomacy AI, which has nothing to do with the combat system.
4) It is inappropriate for the scale of the game.
True, but this doesn't bother me. It's an abstraction, much like the road system.
4) It's prone to artificial tactics.
Most games are prone to artificial tactics, including every TBS game under the sun. Yes, some things may need to be improved, but those are tweaks to the system and not an overhaul of the system.
Let's take your cavalry example. Yes, they can hit and run - much like their tactics in real life. Perhaps the insta-heal promotion needs to go away. Perhaps they need to modify cavalry's attack power against melee troops. But those aren't system problems. As for things like opportunity fire, you can effectively make this so with the proper positioning of your units so that you do get to attack first. That's a decent abstract of the concept of opportunity fire IMO. YMMV.
5) The new problems created with 1 unit are worse than the big stack problem they solved.
This is an opinion, not a fact, and one with which I entirely disagree. I find this system far more interesting and friendly than the stack of doom from prior games. Even moderate stacking has issues (archer or spearmen - which one defends when knights attack?) and I'm not sure there's the perfect system out there. But I know I find this system far, far better than the old one.
I'm not saying there's not a better system out there. But every system has flaws. For example, transitioning from a strategic map to a tactical one has whole host of issues, many of which have been encountered in the Total War games. If you allow players directly to interact with the tactical map prior to combat, then you're looking at some major busywork and will likely bog down the entire game. If you're going the Total War route, then proper strategic positioning often means little to nothing on the tactical level.
And just to answer a couple of other comments I've read in this thread (not all by you, Ohio):
AI Gridlock isn't a product of the system, it's a failure of programming and/or game balance. But you know what? Historically, large armies often do get gridlocked!
If the AI has so many units their entire territory is locked, then that's a programming failure, not a system failure. It shouldn't be possible to do that in the game.
If you can't rush your swords to the front because your archers are blocking the way, then you've failed to position your units correctly. This isn't a flaw of the system, it's your failure as a general.
I like the mobilize/deploy suggestion made by teks and enfo. That helps solve some of the issues while still keeping the engaging combat system.