[lowkey]

I’ve always found it strange that BSM is used for calculating implied volatility of American style options when it was specifically designed only for European style options.

Can anyone comment if there are more suitable models for American style options?

[FabHK]

Generally, you back out local vols (as a function of S, t) of the BS vols (as a function of K, T) by a process described first by Dupire, and then you price American options (and other products that are not sensitive to vol of vol) with that using a numerical PDE solver.

https://en.wikipedia.org/wiki/Local_volatility