Never really understood why it doesn't suit the "character", if by character we mean personality.
Peter has always been shown as a scientific genius who likes making money and gets on well with a wide range of people. You almost have to write him out of his personality if you portray him as not ending up in a high tech job somewhere making big bucks.
Contrast that with writing him as a teacher...yes it would suit him well personality wise as well..but the hours he would need to keep would be too inflexible to fit in Spider-man role. There's a pretty low number of times he would be able to just not turn up for lessons.
What being really successful maybe doesn't fit in with is his branding as "unlucky loser"...we should all be as unlucky as to be young, super powered geniuses, constantly dating good looking women!