Well why not?
You need to adapt to different conditions in Tests. It's part of the job description. You need to deal with rough building up and cloud cover coming and going. You've got to manage with how the pitch is changing, which way the crosswind is going and which side of the bed Mitchell Johnson got out of. Learning what to do when the rain comes in should just be another test of a player's skill.
Half the time it's said that it would produce bad pitches, or that batsmen wouldn't sight properly. But then half the time it's said that bowlers would be the worst affected, having to cope with the loss of grip and a soggy outfield.
So would it be a problem for the players in general? Maybe. But cricket isn't played for the benefit of the players, they're just part of the trade. It's played for the fans. Also Rupert Murdoch, but mostly the fans. And no matter what rainy cricket might be like to watch, it's better than none.
Plus it would lead to endless debate on how best to use the wet conditions. No fan worth their salt wouldn't love the chance to form more opinions after all. Eventually it'd just be another way of making things more interesting.
The way of Test cricket is that you can have a guy standing around for three and a half days who then comes in and wins you the match. Tests are broad, varied and rich and anything that goes against that is missing the point.