Reading what I said again, it made very little sense. I mean in a chapter like chapter 8 in FE6 (Lilina's recruit one), you can make a 7 move mounted unit move 30 spaces in 3 turns with the help of other mounts (two 8 move dudes and a bunch of 7 move dudes), while unmounted units can only punt a unit 19 spaces in the same scenrio, so an 11 space difference over the course of 3 turns (including someone promoting using the Hero Crest in the previous chapter for a 6 move dude)
In FE4 Chapter 10, the distance between Celice and Shanan after 3 turns was only 10 spaces if they moved ignoring all enemies. It's really not that different. It's just rare for players to actually abuse the rescue function. When dancers and fliers get added to the equation, the difference becomes even greater, especially considering the GBA chapter in question doesn't have any places fliers can ignore terrain and just blow the whole comparison in GBA's favour, but I decided to use a chapter that didn't take that into account.
as for not wanting to move your foot units, you don't have to wait for them to catch up to contribute in Chapters 2, 3, 4, 7, 9, 10, Prologue, or Endgame.
Ayra and Jamka can easily help out in Chapter 1 when they're around too (Ayra has more move than everyone in the forest but Sigurd and Cuan whom she ties, and is recruited close to a huge wave of axedudes, and when Jamka is recruited he's pretty much out of the forest). They only struggle in chapter 6 if Celice inherits the leg ring, otherwise they have no problems. They are kinda screwed in Chapter 5 and 8 though.
Staves and dancers exist too but I'm not going to bother going into that too much.