Making Tests 4 days long seems like a great idea. I would support that.
But, 2 innings should stay intact. That's like the pillar of Test format.
Might be hard to cut it down to 4 days then. Might increase the draw rate. It's not a fantastic solution cutting down the innings, but it drastically shortens game time. The other option is bowling friendly pitches, but that's hard to enforce and potentially could be dangerous if taken too far, I don't think some of the pitches provided in the older eras would be tolerated today, they would have been considered a safety risk.
The thrill of a 2nd innings fightback is great, but it's just too rare. The most common scenarios from 2nd innings are that a) it's prolongs the game, game has already been decided in 1st innings, b) Game is batted out for a draw than an actual result or c) The home team having slipped up once, gets the chance to rebat denying the away team a win.
In scenario C, if anything this is unfortunate and often prevents away teams from winning. This was the case for example in the England vs Ireland series. With 2 innings gives both the home team advantage and makes it extremely hard for an upset.
There is also the difference in the 3rd and 4th innings. If the game hasn't been decided in the 1st and 2nd innings, the 3rd innings advantage is massive compared to the 4th. Far, far more so than between 1st and 2nd. That's just an advantage decided by a toss. There are reasons to why choosing to bat second is a good idea, but generally when you bat second, you are going with the fact you expect to bowl the team out early and decide the game in the 1st innings, to where your 4th innings hardly matters.
I've always thought having 2 innings each, the whole point was to give the away team a chance to acclimatise to the conditions as it's harder to click in just 1 innings. But that really isn't the case these days. The inclusion of 2 innings each just gives the home team even more advantage than they already have and gives the team batting 1st advantage too. Which isn't ideal.