I think this is a case where the rules are either simple or complicated depending on how you approach them. Those more familiar with the rules can better see the logical progression, but if you're just jumping in, the collection of rules and decisions can look like a bit of a mess.
The way I think about it, starting from the basic concept and adding practical wrinkles, is as follows.
1) You cannot test the condition of the bunker because that uncertainty is integral to penalizing effect of the bunker.
So by default, you may not touch the surface of the bunker. But to play the game, you have to be able to address the ball... so
2) You can walk up to your ball and take a stance, but you cannot take any action beyond those reasonable and necessary to address the ball. You can't ground your club because that's not necessary for making a stroke.
This is fine, but as Fourputt and others said, it can be dangerous to approach or walk around in a bunker. The rules are important, but it's more important to avoid injuries. So
3) If you slip or fall, you're allowed to do whatever it takes to avoid injury, even if this involves touching the sand. (But if you move the ball or affect the lie, you're still on the hook.) It would be unreasonable to penalize someone for having reflexes.
And this is all great, but especially when playing with a shared cart, a golfer can save a lot of time by bringing more than one club with him. If he has to keep all his clubs out of the bunker, it's going to mean a lot of walking back and forth. That wastes time, disturbs the bunker because of the extra traffic, burns more time cleaning up the footprints, and still gives the golfer additional information about the conditions because of the extra walking around. So...
4) You can set your extra clubs down in the sand.
I think it's a fairly logical progression. The exceptions to the "don't touch the sand" rule are either necessary to playing the game, or are both beneficial and easily distinguished from acts that might be construed as testing the conditions. E.g., you could allow grounding the club, but then you have to make tough calls as to whether a golfer pressed more than he was entitled to, etc.