A good question. Interesting, it seems that gemora and meforshim are not even suggesting that we follow that practice.
Could it also be that this was before having siddurim and maybe even before having a fixed prayer? So, then preparing would be more extensive to make sure your prayer goes well.
To expand on your question, Bava Kamma 30 says that hasidim used to be extra careful not to do something that hurts other people. Nobody drives like that anymore. When did this change?