I'm not just looking for a bank that does the standard stuff somewhat better, or is nicer to me. There is a lot more that could be done. Wealth management related startups like Mint have scratched that surface, but with an end to end implementation of a bank and all the tools and data that brings, a lot more becomes possible.
Also, First Republic's site looks like something made with a table layout in the 90s and left alone since, so I doubt that they're doing anything innovative on the consumer facing side that requires any amount of tech expertise.
Admittedly my finances are pretty simple, but my bank is something I really don't want to think about much or spend a lot of time dealing with. Maybe if someday I have a lot of wealth to manage I'll feel differently. The most important thing is that I can always get somebody on the phone right away that is informed and helpful.
First Republic's web tools aren't going to win any design awards but they do the job and have never given me any trouble.
Also, First Republic's site looks like something made with a table layout in the 90s and left alone since, so I doubt that they're doing anything innovative on the consumer facing side that requires any amount of tech expertise.