Then rounds, they should last 10 seconds, but they're often a lot faster, see:
I see that a few months ago rounds went from 5 to 10 seconds, so I'm asking wouldn't it be better to have 1 minute long rounds?
Share difficulty is set so that they will be found every 10 seconds
on average. Just as with bitcoin blocks (which are supposed to be found every 10 minutes but are often found 2-3 minutes apart or 25 minutes apart), there will be variance in how frequently the shares are actually found.
An average of 1 share per minute would be accomplished by making share difficulty 6x higher. That would increase variance for any given miner (which seems to be the opposite of what you are looking for).