me too
it is just totally possible, there are so many web api-s, you just need to be a good programmer and study a lot
you will not really find or use big web apps because
1. most companies have already built their native apps with mobile engineers
2. web "programmers" or rather designers are stuck with old tech
3. web apps will start to become strategic targets(!) by most developers/companies if you are sure they are cross platform (which was crippled by Apple and now they even try to eliminate modern web capabilities on iOS