These are exactly another set of bad old combos, and the fact that their use is widespread is just another example of how bad very common things are:

  -  it doesn't make sense to have a/e as beginning/end, there is a symmetry in the commands, but there is no symmetry in the a/e keybindings, they are on different rows

  - likewise, it doesn't make sense to use the less convenient ⌃ for such a frequent command (and this is also the rightful criticism of all the bad Emacs pinky defaults)

For example, you could use right ⌘ (a thumb key) as your text movement key (or even Space), then you have home keys

  - JKL; for cursor movements and

  - DF for your word movements (instead of having to move your whole hand to ⌥◀/▶)

  - A/⇧A for line start/end movements or maybe A/G if it's frequent enough to not warrant using ⇧

And then that would match your text editor keybinds, so you don't have to waste time remembering platform-specific keys.

And re. those other apps - it's better to rebind them all (or, rather, use a tool to have the keybinds work in all of them) as well to use something good rather that stick with the bad just because someone lacked good design chops in the past