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Mobile OSes will ask (and act directly, if ignored) backgrounded apps to dump themselves out to disk to reclaim memory when needed, and the kinds of processing you’re allowed to do while backgrounded are quite limited.
There’s really not much of a performance reason to kill backgrounded apps. Feel free to kill them for other reasons, like unnecessary network traffic or draining your battery by keeping GPS active.
Running Android 14 and somewhat disagree. I have had 1-2 games running in the background after "exiting"/"quitting" the game and dropped from 80-90% battery to 30% in less than 2 hours. (GPS and Bluetooth both disabled). Battery dropped as though I was actively playing with the screen on during that time.
Killing apps has helped me with this issue, in general. However, for the offending game, setting "app battery usage" (specific to Android, not sure of iOS equivalent, if any) has helped better for this issue. Seems a lot of games are trying to load unmecessary stuff and/or sell usage data, despite exiting the game...