What if; when a player upgrades the stamina of their mount it also gives your mount the capability to swim for a few seconds?

Now I don't think that mounts should be given the ability to swim far distances. I'm talking maybe three seconds max, just enough time so you aren't forced to dismount when crossing a small river that is just a tad to wide to make a jump and a tad to deep to walk across. I've lost count of how many times I've tried to cross a river thinking it was shallow enough for my mount only to be dismounted for a hot second. Then remounting to continue on my ride through the country side.

To be honest it's not really an issue, it's not immersion breaking or anything. I'm just curious to see if this is something that interests people.