What are the Pro's of doing this?
It's mostly a playstyle and immersion thing.
I've always held to the notion that most high-level npcs are fairly well-known, and the same logic applies to high-level pcs. When a new 15th level pc enters the party, where have they been all this time? How come, all those times the pcs went looking for a wizard for hire in the same city, they never found this guy who was, apparently, sitting around waiting for them to need him?
In addition, it makes a high-level pc an achievement rather than simply a given. I don't know if you've ever played Paranoia, but if you're playing a classic or 'zap' style Paranoia game and your character ends up advancing to Green security clearance during actual game/campaign play, it TOTALLY makes you proud. You feel as though "ACHIEVEMENT UNLOCKED!" Old school D&D was kind of similar; if you got a 1e pc from 1st to 10th level, that was a heck of a thing. I like that feeling.
I can clearly remember a few Con's from back in the good old days.
[*]1st level PC sits in the back during any dangerous situation twidling thumbs for multiple game sessions
[*]1st level PC gets killed by any area effect attack on the party, doesn't matter if he saves.
[*]Either the DM takes it easy on the new PC or he pretty much just dies to the higher level threats.
I run a pretty hardcore sandbox, so the pcs can pick their challenges and choose whether to address the low-level guy's low level status themselves or not.
[*]The new PC levels up pretty fast anyway from the huge amounts of XP, so why bother.
This is a feature, not a bug.
As for "why bother", you could ask that about literally anything in play. Why bother tracking arrows and rations? Why bother with encumbrance? Why bother with language issues? Why bother roleplaying your character? Why bother making the pcs check for traps, instead of just checking the DC against their trapfinder's skill? I really don't think this is a meaningful question when the answer is quite clearly playstyle preference, and I think it's laid out pretty well in the OP.
This also might not work as well for a converted adventure path.
Probably not, at least not without a lot of sidequests and expansion. But I run a homebrewed campaign, and when I integrate published material, I hack and alter it pretty severely. (I've actually been twining the 2e adventure
Dead Gods into my 4e game since about 3rd or 4th level, and the pcs are mid-20s now. I have hacked the crap out of it, changing details, using exactly none of the encounters in the original, rewriting a lot of the basic story, etc. to suit my game.)
I could see this making players more tentative both because of dying in the first place and starting over as well as being fragile compared to the rest of the party.
Possibly. As I said above, the pcs imc have a significant amount of influence on what challenges they face, so they can definitely choose their own adventure (if you will).