The only drawback to Take Lanes is the real estate that they take up.
In my studio there will almost never be more than 5 takes so it's not really a problem. If someone can't get it by then we move on.
If we decide to continue with more takes, the previous ones are deleted. No reason to keep crap that will never be used.
There are also times where a track is put together piece by piece. On those it works similar to the above. Delete the crap, keep what's good. So there is never more than just a few takes ever.
I never use the mute tool. I comp by splitting clips, and moving them to a new lane. Once the track is comped, I may delete all other lanes unless there is something there that I may want.