Get ready to be shocked....
I don't like the short skill list. (I consider that a step backward in PF as well)
I am not shocked, it was what I expected. But liking that or not, you can still see the context from which I am arguing.
But why is it that anyone playing 4E is required to agree with you that EVERY character will ALWAYS gain something in EVERY skill?
Did you like or dislike saves and BAB increasing with level in 3E? Or similar things happening in earlier editions with THAC0 and saves?
I think it's just an extension of that. Maybe you would prefer if Reflex Saves were also a skill. I believe you could only create a reasonable system for having "skill points and skills for everything" if you also have a mechanic that defines how you gain skills by using them, or explicitely training them.
If you don't have all that...
1) For "believable" advancement, they need to track skills used on their own to argue that certain skills should be improved. (And if they didn't want "believable" advancement, why not go with the +1/2 levels anyway).
2) Players have to manage a lot more minitua as they have to remember all skills they may find important. I often find this problematic in games with extensive skill lists, as you have to check manually whether there is a skill you may need to actually describe your character's vision and advancement correctly. "OMG, my Secret Agent didn't take Perception! Why did no one tell me I would need that!" Or "Oh damn, Will Saves! I forgot putting any ranks in that since 3rd level! Oh noes!"
And of course, the opposite will also happen - min/maxers will carefuly select which stuff to take. "Okay, I never ever will use weapons, so no reason to raise my staff skills and I'll put those point into arcana".
The freer the advancement of the character, t he more chances for imbalance - characters with glaring weaknesses or characters with optimized min/maxed builds.
3) Also, another risk is that with a too detailed skill list, you can't even create characters with "reasonable competence" in skills that you expect them to have. If your resources for improving skills are limited, you will at some point need to make choices were to invest.
In 4E, you can fare reasonable on an untrained skill since you have ability score mod + 1/2 levels. In 3E, you can have a 5 point difference by 2nd level, and it only grows from there. (And mind you, this is not about making the character that can do everything - but just a character that has a reasonable chance to do some of the stuff you associate with the concept, without being a master at it.)
But we were talking about CLIMB as the example.....
Climb is a perfect example for an adventuring skill. Of course you get better at that from adventuring, because you travel through the wilderness and through dungeons a lot and have to climb stuff occassionally!