I think more focus needs to be placed on the DCs and not on the skills list and the bonuses. It seems that the journey is the less agreed upon aspect while few complain about the destination. No one is complaining about whether a typical lock is DC 15, DC 16, or DC 19. It's the skill aspect that causes grumbles.
So the DC generation system should be the core while the skill rolling aspect should be modules.
So the core says a typical lock is usually DC 16. Everyone gets that. The DMs and players both agree with that
1) DM 1 is using Skill Training +3, with smaller skill list, and the suggested ability score and skill. The player says "Salamander Stu uses his knowledge of Barlian crafts to unscrew the loadbolt in the lock. So DM 1 calls for a Dex check with a +3 bonus from Stu's Open Locks skill.
1d20 + the thief's Dex + 3 (Open Locks) vs DC 16 lock
2) DM 2 is using straight Ability checks with the ability score he feels appropriate. The DMG warns that characters will fail often. The player says "Salamander Stu uses his knowledge of Barlian crafts to unscrew the loadbolt in the lock." The DM calls for a Int Check.
1d20 + the thief's Int vs DC 16 lock
3) DM 3 is using Skill Training +3, with the large skill list, and the ability score and skill she sees appropriate. The DMG warns that the players will rarely get their skill bonus but frequently get to use their best ability scores. The player says "Salamander Stu uses his knowledge of Barlian crafts to unscrew the loadbolt in the lock". So DM 3 calls for a Int check with a +3 bonus for Stu's Barlian Lore skill.
1d20 + the thief's Ability mod + 3 (for the skill) vs DC 16 lock
4) DM 4 is using straight Ability checks with suggested ability score, bell curve rolls, and bonus from class not skills. The DMG warns that characters will often often fail hard checks and success easy ones. The player says "Salamander Stu uses his knowledge of Barlian crafts to unscrew the loadbolt in the lock." The DM calls for a Dex Check plus Stu's +3 bonus for being a warlock.
3d6 + the thief's Dex +3 (warlock) vs DC 16 lock
Have the part we can sort of agree on have the most focus. Allow everything else about skills to be variable.
So the DC generation system should be the core while the skill rolling aspect should be modules.
So the core says a typical lock is usually DC 16. Everyone gets that. The DMs and players both agree with that
1) DM 1 is using Skill Training +3, with smaller skill list, and the suggested ability score and skill. The player says "Salamander Stu uses his knowledge of Barlian crafts to unscrew the loadbolt in the lock. So DM 1 calls for a Dex check with a +3 bonus from Stu's Open Locks skill.
1d20 + the thief's Dex + 3 (Open Locks) vs DC 16 lock
2) DM 2 is using straight Ability checks with the ability score he feels appropriate. The DMG warns that characters will fail often. The player says "Salamander Stu uses his knowledge of Barlian crafts to unscrew the loadbolt in the lock." The DM calls for a Int Check.
1d20 + the thief's Int vs DC 16 lock
3) DM 3 is using Skill Training +3, with the large skill list, and the ability score and skill she sees appropriate. The DMG warns that the players will rarely get their skill bonus but frequently get to use their best ability scores. The player says "Salamander Stu uses his knowledge of Barlian crafts to unscrew the loadbolt in the lock". So DM 3 calls for a Int check with a +3 bonus for Stu's Barlian Lore skill.
1d20 + the thief's Ability mod + 3 (for the skill) vs DC 16 lock
4) DM 4 is using straight Ability checks with suggested ability score, bell curve rolls, and bonus from class not skills. The DMG warns that characters will often often fail hard checks and success easy ones. The player says "Salamander Stu uses his knowledge of Barlian crafts to unscrew the loadbolt in the lock." The DM calls for a Dex Check plus Stu's +3 bonus for being a warlock.
3d6 + the thief's Dex +3 (warlock) vs DC 16 lock
Have the part we can sort of agree on have the most focus. Allow everything else about skills to be variable.