Tetris is already kind of like that. My version avoids dropping the same piece consecutively (re-roll once on duplicate) in order to get a more realistic Tetris experience.
I have three randomizers in my version here: https://www.susmel.com/stacky/ you can switch between them with a t on your keyboard (no phones, sorry). If you expand controls with c you will see which one is active. NES and 7-bag are in there as well as "random"/stacky one. Shift+enter in the main menu to pick a level to start with.
I wish I had bookmarked the incredible deep dive into the multiple algorithm schemes for Tetris piece picking and which families of the game used which algorithms and why. The modern standard (as now dictated by rights holder The Tetris Company) is a bag approach, but has interesting nuances. That one I believe is 7-Bag these days (7-Piece bags). I've also heard a lot of love for 35-Bag which is the approach used by Tetris: The Grand Master 3. (From what little I know about it, TGM is a fascinating "family", especially its use in both tournament and speed running cultures. But because of all the usual drama of Tetris it can be sometimes hard to play TGM in the US as the license holder is Japanese.)