I'd be in favor of removing all spells that give flat buffs to skills without doing anything else. However I think a better solution would be to allow spells to increase the utility of existing abilities. Say have the jump spell half the DC on all jump checks instead of just giving a flat bonus and count all jumps as having a running start. This results in a spell that allow joe shmoe to jump reasonably well and turns someone invested into acrobatics into a super smash brothers character. It keeps the spell as a strong utility option without invalidating either the wizard or the acrobat. Unfortunately such and approach will require going through and adjusting each and every spell on the list. Though at least for skill bonus spells halving the DCs is a fairly easy quick fix.
I agree with your concept.
I would prefer instead of halving the DC, double the bonus (including stat), and possibly negate armor and and encumbrance penalties. Helps those who don't have the skill points invested, and rewards those who do. (note: There would be issues with doubling 0 or negatives. Not sure of a good solution to that so halving the DC may be the more elegant solution.)
Things like fly and spider climb that bypass skill checks altogether I see no issue with. Mundanes climb, Wizards ascend.