I'm definitely on the opposite side of the fence here. Like you said, one really has to pick and choose what makes sense for their playstyle. At least in my case for example, I'm willing to sacrifice AC for skill-points whereas others may choose that AC is more important to them. My day-to-day gear is what I wear adventuring as well as RP with the exception of being in Disguise (which makes sense as you wouldn't wear your regular clothes here!). Having that ability to make the choice and a system of 'pros and cons' gives us better character diversity and allows people to focus on what's important to them while neglecting other aspects through conscious decision.That's part of the issue, though.
You want to portray your character has acquired a certain proficiency in a given skill over time. So you use items to showcase that. Though some/most of those items are not the ones you will be wearing day-to-day. You put them on when you need to showcase your character's proficiency with e.g. Lore: Arcana. If you are then caught in a situation without those items on, and need to use your Lore: Arcana skill, you are suddenly less proficient than you ordinarily would be.
You could of course pick items that give skill bonuses, while also providing the other bonuses you are after. That's what several people try to do at least. There are downsides to it, however. Typically either reduced skill bonuses, attribute bonuses, armor, or spell slots.
I think that would be a DM team decision but I also don't feel like 'all DMs do DM equally', nor do I believe they are expected too. A DM may run an event and ask their participants to make a skill roll with a "DC" they have set in their mind. Another DM, may ask characters to take the same action a few days later but set a different "DC" for success. I will outright say that I have -no- DM experience at all, but I'm going to guess that there is no 'master skill sheet' that tells DM's what "DC" an action takes, nor do I think they keep track of DC's other DMs have set in the past-- I think its a DM judgement call and its up to the DMs discretion whether something ultimately passes or fails..... I think???First it would require every DM to treat the rolls the same way, as otherwise a character is a master in one event, and a simpleton in another, despite no changes to the character.

I agree with you here and your totally right, showing people the breakdown of 'Natural skill + equipment skill' will be really divisive and cause alot of disagreements. Good call!Second it's gonna be highly divisive to the player base. Some will find it unfair that they efforts to acquire equipment is not taken into consideration, while others will find it unfair equipment outshines their natural proficiency.
I don't think we should consider combat mechanics as a different choice against other skills. If you choose to focus on combat in leu of RP skills, or vice versa, you have decided that this is what's important to you. Both options should be available depending on what sort of experience your looking for playing the game. Those who want to focus on RP/high-skills should have that option to do so, in the same way that those solo players who constantly speed run Skull Gorge have decided that is what's important to them. Also one can always choose to be 'decent' at combat and 'decent' with skills if they would prefer to be good at both just not 'exceptional' at one.Third if DMs agree to only consider the Natural part for events, then equipment with skill bonuses become worthless for events, which is one of the main reasons to invest into a skill in the first place (combat mechanical skills are a different thing entirely).
I guess what I'm trying to say is its ok to not be 'max' at something and still be considered to have a very high proficiency in a skill-- your just not going to be 'as good' as those who really have gone 'all in' for those skills. We shouldn't limit players who do love focusing on skills by preventing them from being the 'best in their craft' just because their peers don't want to 'sacrifice the equipment slots' to be at that level.
If 'speed changing' gear just to have a higher dice-roll is really that big of a problem (which I'm not really seeing people do this in game), maybe there should be a delay on equip/unequipping (Like that greater restoration spell, 30% 60% 90% ). This would be a super unpopular so I'm not suggesting it for fear of being locked in the Flaming Fist Prison for all eternity by the player-base*laugh*.
By putting limitations and caps on the amount of skill points a player can have (outside of what the game already does for us today) we are just taking another step towards making everyone feel more vanilla and less exciting.