Personally the thing that bothers me most about American accents with these languages is failure to make diphthongs out of adjacent vowels. An American accent will stretch a Romance diphthong out into lengthy syllables. For example in this audio link above, the speaker says hodie has "HOE-dee-ay". I speculate someone more used to speaking a Romance language would say /'hodje/, two syllables. (I note English wiktionary has it as 3 syllables. Not sure what an ancient Roman would do.)
In any case I think a lot of the confusion is orthographic in nature. An English speaker is used to an <e> being /i/. It's not that they can't do an /e/ sound if they tried. A lot of people in the US also have very little real exposure, eg. we have language classes in school where making a real attempt to drop our accents and interact on a level plane with natives is never even seriously considered, it's just a place to hold you in a desk and fill out worksheets.
The US education system is incredibly diverse--as is the US as a whole. That may the case in some schools, but it's certainly not the case everywhere. My southern high school was suburbun/almost rural and had enough kids on free lunch to qualify as a low income, but my German classes were extremely intensive. The French and Spanish classes were no joke either.
And in much of the country almost everyone will interact with native Spanish speakers fairly often.
Even RP has some pure long vowels (e.g. NURSE, THOUGHT, BATH). FLEECE and GOOSE do tend to be realized as narrow diphthongs, though.
In my own accent (Scottish), except for the four diphthongs (PRICE, PRIZE, CHOICE, and MOUTH) of which the first two are allophones, all the other vowels are pure. I verified this while developing a formant speech synthesizer.
All of them?
