Does the faster player get nothing in return for their speed advantage? If so, then shouldn't they just play slower? If not, then aren't they compensated fairly for the risk of running into a difficult sequence earlier in the game?
In Guidelines Tetris, you only deal damage if you do a sufficiently complicated maneuver. A Tetris (4-line clear), a T-Spin ("spinning" a T-block into place), or a "Combo" (repeatedly clearing lines non-stop). As such, you only can do a major damage from I-blocks (a 4-line clear / Tetris), or T-blocks (TSpins).
No other block in the game can deal major damage by themselves. So the placement of I blocks and T-blocks is fundamental.
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Also note: Garbage is a "comeback" mechanism: large amounts of garbage "feed" the opponent lines to perform a combo with. If you deal non-lethal damage to the opponent, it is common for the opponent to use the garbage you sent him to "combo" into a large amount of damage back to you.
As such: the game becomes more garbage is sent around. There is a chance the opponent can see a 12-combo through the garbage you sent them. Its difficult for the untrained players to see combos, but it definitely comes into play at higher-levels.
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The current system (including the bag-randomizer) has been carefully balanced between many issues, and playtested for years. Aside from occasional issues (ex: TSpin singles becoming too easy in an early version: leading to the development of "TSpin Minis" to nerf that technique), the overall Tetris Guidelines rules are quite good. I recommend playing a modern competitive version of Tetris and trying it out yourself.
Combo-play is definitely considered one of the strongest strategies right now. Moving to a true-randomizer will necessarily nerf Tetris / T-Spin play, because you can no longer predictably get Tetris or T-blocks.
In my experience, most players want to play Tetris: that is, create Tetrises (4-line clears). Combo play is certainly fun, but it makes sense to "buff" the canonical "Tetris" strategy of the game since that's what people expect. Tetris is the name of the game after-all, and you can only play "Tetris" if you have some kind of assurances that I-blocks are on the way.
Nerfing Tetris and buffing Combos seems to be the wrong direction for balance. If anything, Combos need to be nerfed.
Perfect-clear play is also lovely to watch. Computers are better than humans, but when a human perfect-clear player comes in, its truly intense and fun to watch (and play against). Perfect-clear play relies upon the bag-randomizer to a severe degree, and isn't even that strong of a strategy (a good perfect-clear player needs to threaten 3x perfect clears within 20 seconds to be competitive at high levels). Moving to "true random" would erase this obscure style of play completely.
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In any case, there's a big community which prefers to play with true randomizers: the "Tetris Classic players". They play by a separate set of rules entirely.
As a Guidelines Tetris player, I obviously have my bias. I think the game is more fun with Tetris, Combos, and Perfect-clear openings in play.
Only if T-blocks and I-blocks come. If there's a drought of T-blocks and I-blocks, then the combo-player wins.
Combo is currently the strongest strategy, under the current Tetris Guidelines.
If you have "too many" I blocks, you run out of Tetris room very quickly (You can only form a Tetris if you've built up 4-rows of 36-minos, with the last 4-square hole being where you use the I-block). If you have "too few" I blocks, you literally can't clear the hole and die.
My overall point is that the bag-randomizer "buffs" Tetris and T-spin players, while "nerfing" combo play. I argue that Tetris-players are the "main strategy", and probably should be buffed to be stronger.
Tetris players also get wrecked by t-spinners as t-spins do double damage compared to how many pieces you clear. The t-spin is the only piece that can send 6 lines back. And with about three bags worth of pieces you can do a t-spin triple + t-spin double + t-spin single = 12 lines.
Only way you can top that is with three all-clears which you most likely won't get.
With the current rules, if you wanna win, you gotta be either t-spinning or comboing in pvp tetris.
You are correct in that TSpins are a great upstacking strategy. Tetris however is a downstacking / defensive strategy.
Consider a "Counter-Tetris": You clear 4-lines of garbage, while dealing 4-damage (+B2B). That's a "effective garbage differential" of 8-lines (+B2B) (you lost 4-garbage, while dealing 4-damage to the opponent). This ideal doesn't always happen, but its far more powerful than a TSpin Triple.
It is impossible to build a TSpin Triple out of garbage, you MUST create a specially crafted overhang. TSpin Triples always leave an overhang. As such, TSpin Triples and TSpin Doubles can at best, clear 1-line of garbage. (and a TST will block your garbage hole until the TST is executed AND the overhang is somehow cleared).
TST into 1-line of garbage is 7 "garbage differential" (2-lines of upstack, 1-garbage cleared + 6 damage sent + B2B). TSD into 1-line of garbage is 5 garbage differential (+B2B) (1-line of upstack, 1-garbage cleared + 4 damage sent + B2B).
Counter-Tetris is 4-garbage lines cleared, 4-damage sent+B2B (8-garbage differential). 3-garbage lines cleared is 7-differential, and 2-garbage lines cleared is 6-differential.
As such, even a 2-garbage + 2-upstack Tetris is more "garbage differential efficient" than all TSpin Doubles, while a 3-garbage+1-upstack beats a pure-upstack TSpin Triple.
Just don't upstack a Tetris, and you'll do fine. Upstacking for a Tetris is grossly inefficient compared to Upstacking TSD or TST.
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My recommended strategy is: TSD for upstack, Tetris for downstacking. TSD keeps the "hole" open for an emergency Tetris if the opponent starts to spike you (an incoming I OR T block can be executed).
A TST overhang blocks the hole however forcing ordering. (you MUST use a T-block), and the overhang will block the I-block until you clean it up somehow.
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Anyway, I argue that going for Tetris should be a stronger strategy... because "Tetris" is literally the name of the game. The "namesake" strategy is weaker than people expect as it is, weakening it further by using a full-randomizer would probably be a bad idea.