Technically yes a bow might be firable in one (three second) round, but you have to locate and get the arrow, get the nock lined up with the string, make sure the cock feather is pointing away from the bow (or it will catch when you fire and either strip off or knock the arrow - either way the arrow is going nowhere near your target), secure the nock on the string in the right place, draw and aim the bow (which itself takes longer than 3 seconds even when you don't really aim properly) and release the arrow. Compressing all this into a 3 second process, even with modern equipment, means your penalty would be massive, if of course we were shooting in the real world . You could probably get this faster with practice, but it's still not easy.
We often do 30 second speed rounds at 20 yards. I consider myself to be doing well if I get 6 shots (starting with an arrow on the string, so 6 seconds per shot). People who are very good can easily do 10-12. At the high end of that, you are shooting every 3 seconds. This is certainly shooting at a penalty - not as accurate as taking time to aim. I still get my arrows on a 3' target, just maybe not the scoring part of it. Experts will still be getting a lot of bullseyes. But that's with a static target, at close range. Stack up the penalties and that will change.
Partially you get faster due to practice. You know where the arrow is when you are reaching for it. Having the right equipment helps, as well as familiarity with it. A side quiver is faster than a back quiver (slightly), arrows need to be loose, etc. With practice you can basically just slap the arrow down on the string. The orientation of the feathers is not important enough to bother with for 20 yard shooting, during a speed round. Perhaps this carelessness contributes a bit to the penalty, especially if the range is longer.
In practice, a less skilled archer will simply be unable to shoot at the fastest speeds. As a game mechanic, I don't think it is worth a separate mechanic beyond applying the activity penalties.
If rounds are really short, I think it might make more sense to make 1 shot per round the standard, with all modifiers assigned on that basis, and then have an "aim" action the player can choose to reduce the penalties. People are strangely more excited about computing bonuses than penalties....