As such, people are aware that you just have to know how to pronounce every particular word, rather than relying solely on orthography.
Anyway, your example isn't very good: "light" and "lite" are homophonous anyway.
A better one would be "calm". The "l" is almost mute. Presumably, one could "simplify" the orthography to "cam". And you would pronounce "kom" or "kam" according to context.
I claim one of the pronunciations would eventually disappear, sooner or later.
If you're asking for a "scientific study", I don't have one and I don't even know where such a thing can be found.
But the country I'm from has had 3 orthographic reforms in the 20th century. The last one being all about removing supposed "mute" consonants - but which acted like accents in that they altered pronunciation of the word.
is there any evidence for that?
anecdotal evidence in english for example suggests just the opposite: light -> lite, etc
however learning a language as a child growing up, vs as a second language later are quite different, and the dynamics that affect language change are hence very different too.
http://jbr.me.uk/ranto/m.html explains how esperanto is unlikely to change, and also why that would be a good thing.
back to your argument, i don't think the words with different pronunciation would be lost, but certainly the language would be harder to learn.