It's not just the schedule though, it's a factor yes, but it's far from the full story. Fact is, most of England's back up seamers in the test side just don't have the tools to be good ODI bowlers. Finn is the only person outside of the test line up who is a really good ODI bowler. You could argue that the schedule means they turn into more FC specialists, but the limitations they have in the short format are all pretty natural ones IMO. Either too skiddy (Meaker, Onions) or too slow (Tremlett, TRJ) or even both (Woakes). Now you could argue all of the first four could improve significantly by developing one day tools, such as slower balls, more variations in length etc, which is your point I guess. But none of them are natural limited overs bowlers.
It really hinders England as an ODI side, as people are always wanting the big guns to get rested etc, but the replacements just aren't up to it.
It's a massive contrast to Australia funnily enough. Of their five frontline quicks in the Ashes, squad, only Starc will likely make the ODI squad (although Harris has basically had his ODI career ended by fitness issues, not a lack of ability). Means they can give rest to all their best test bowlers, and reel in replacements such as McKay, Johnson, Faulkner and Doherty and not hinder their side. I wouldn't be surprised if Australia win the ODI series, not because they're strongest XI is better than ours, but simply because Anderson and Broad won't play the whole series.
On another note, I think Graeme Swann's ODI career is done. No spring chicken anymore, and Tredwell has shown himself to be a much more than adequate replacement. I think England should really be trying to get Briggs into their limited overs set up as well. With Swann's recurring elbow, and the fact that he's had several other injuries of late, I just think there's no point him playing in coloured clothing anymore (maybe T20's). And I think the English establishment are starting to agree (reckon he just wasn't selected for the CT knockouts, not injured).