Maybe the problem is not bridging the gap between 300 and 1500 but in our twisted way of thinking that's slowly been creeping on us over the years.
We live in INSTANT world. Dunno exactly how we got here, but evereybody wants to do something over night. Get rich over night, become celebrity over night... Become an airline pilot over night...
You can try to become instant celebrity and there is no danger in doing it (with the exception of losing dignity - but to some people today it seems to be overrated
).
I just think there's much more at stake (besides your dignity) if you start your aviation career like that.
Just ask any of the old timer pilots (or not so old ones) how they started their career. And after how many hours of skydiver runs, air taxis, instructing, days hanging on the local airfield just to get a sniff of burned 100LL have they landed a first airline job...