Since this is now about "How to improve Unleashed-style gameplay", let me throw in my two cents:
Personally, I thought Unleashed was the best of the three when it came to Daytime gameplay. Yes, there were too many of the "oh look it's those three robot things time to quickstep for a full minute" sections, and while I like the QTEs, they don't particularly fit. However, what it didn't do that I felt harmed the others, was try to shoehorn traditional platforming in. The platforming doesn't complement the boost mechanic, it overrides it, and you're left with a game split into sections that require two entirely different skill sets, thus feeling like two entirely different games.
While one solution would be to throw out the boost gameplay and focus on the platforming (essentially the "Let's go back to Adventure and try again!" solution), let's do the opposite. Let's throw out the platforming and focus on the boost gameplay.
After all, Colourationleashed (that doesn't work; I'll call it Unleashed/Colours/Generations, or UCG) isn't a traditional platformer. It's a racing platformer. Instead of focussing on platforming, it's centred around a limited boost mechanic, jumping between paths, and navigating an environment to get to the end of a level as quickly as possible.
With that in mind, which games should we look at for inspiration to improve/innovate Boost!Sonic gameplay?
How about Nitronic Rush and Distance (Refract Studios)? Where UCG are racing platformers, NRD are platform racers. NRD is centred around a limited boost mechanic, jumping between paths, and navigating an environment to get to the end of a level as quickly as possible.
Sound familiar? Good. All of these games are at the intersection of platforming and racing; and share many level mechanics too (NR has a section where a road fills with rolling spiked barrels that closely resembles the similar section in Rooftop Ruin, for example).
So what can Boost!Sonic take from NRD? I'll posit a few things and try to solve problems with them as I go:
A1. Death. When your car is destroyed in NRD, it is immediately returned to the last checkpoint, with the timer still running. (When I play, it happens a lot.) There is no limit on how often you can die. The lives system is an incredibly outdated concept for a game with a save system that only puts you back at the start of the level when you game over anyway, and only serves to frustrate the player by making them repeat a large portion of the level whenever they fail one section a few times. Instead, reinforce the idea that death does not impede progress, it only affects your scores; death happens.
To keep death relevant, see B1.
A2. Boost availability. No, not less. NRD's boost system effectively gives you full boost at the start, as well as whenever you go through a checkpoint or die, and also refills slowly over time or when you do tricks. Since boosting is the main mechanic of the game, and progress is slow without boost, an expert player should be able to boost his way through the entire level without running out. While UCG has generally managed this, there are usually situations in which the boost dries up. I feel the boost should regenerate, allowing the player to get back in the game quickly, and perhaps have multiple attempts at reaching a high path or similar scenarios.
A3. Game modes. NRD, like many racers, has time trials, multiplayer races, etc. If we're going to have a racing platformer, we should let people race. Consider catch up mechanics (e.g. the leading player burns through boost more quickly etc.), include a replay system... essentially, the multiplayer lobby should resemble that of a racing game. The goals could vary (see B1), but the basic scenario is the same.
A4. Custom content. NRD comes with its own level editor, allowing users to create and share their own levels using the content available in the game. Most of the games played in Distance (although still in alpha) are played on custom tracks. Custom levels have extended the life of Generations PC significantly, and this is with user-created mod tools. Investing in making a proper editor with a hub that allows the levels to be shared and played would reduce the number/amount of original levels as well.
But there's no need to stick to NRD. A few other suggestions:
B1. Scoring. Sonic Colours is probably my favourite game of the three despite enjoying the actual gameplay least. Part of this is through offering the Egg Shuttle, which means I can just play through the entire game in one go; part of this is the deliciously broken Super Sonic, which is how Super Sonic should be; but a good amount of it is the scoring system. It's flawed - it focusses on Wisp usage far too much - but it means that earning an S-rank isn't as simple as playing through the game as you normally would. It also keeps track of your best score, time, and rings...
... so let's separate them and make them three separate targets. Within every level, if you score 50000 points, finish within 2:30, or collect more than 250 rings (numbers used purely for illustrative purposes), you receive a bonus of some kind. Maybe hitting all three targets (not necessarily on the same playthrough) earns a Chaos emerald, with the obvious Super Sonic reward for collecting all seven.
Multiplayer could be set up in order to do best in one of these three targets, or even all three (a la Sonic 2).
B2. Traditional platforming. So, it doesn't fit in our "new" Sonic. But we don't have to throw it away - instead, make it a separate game. Could be a (2D) Sonic 5 or a (3D) Sonic Adventure 3 (or both) separate from the UCG games; could be a spinoff with Tails, Knuckles, or Amy (if Captain Toad can get his own game, so can Amy); could be an entirely different franchise altogether. It could be alternated with UCG, or given to a different team, or UCG could be given to a different team etc. - but there's no reason having one style of game needs to preclude others.
None of these dramatically change the main gameplay; at most they are additional modes or tweaks. What needs to be accepted is that this is
NOT Sonic the Hedgehog as known in 1991; so instead of holding it to the gameplay ideals of those games, focus on making it good in its own right.
... That post just kept going. More than a thousand words? I didn't even include the big bit about exploration...