Did non-rhoticism in England develop because...

It became bothersome having to vocalise an "r" that didn't precede a vowel? That it sounds better?

In the UK at least (well, in England definitely, but not here in Scotland) the letter "r" is missing in the pronunciation of many words when in fact it should be voiced, but as Josh says it's so much easier to glide over it. "Art" (or artist) is an excellent example. But very often an "r" creeps in when it shouldn't as it doesn't form part of the words concerned - eg when one word ends with a vowel sound and the following word starts with a vowel. In that case the "r" gets tacked on to the beginning of the second word - eg "and here is the work of another artist" comes out as "and here is the work of anothuh rartist", but if you sat them fast enough you wouldn't really notice the difference.

An illegal "r" often creeps into the middle of some other words such as "drawing" - "here is a very nice drawring...."

Where I live, there is no non-rhoticism or intrusive r. There is sometimes an intrusive L, though. I've heard "dralling" before.

I'm from the Pittsburgh area and many people say things such as "drawling" for "drawing" here as well. Some people will often say something like "I sawl him yesterday."

How does l-vocalization affect that?

I think an intrusive L would be likely to originate in a dialect with L-vocalization, in the same way that the intrusive R originted in non-rhotic dialects.

I completely disagree that one has to vocalise "r" if not followed by a vowel. You are still perfectly well understood, and RP tries to rid itself of the intrusive r. Most German dialects do this too and omit r and replace it with the "ah" sound, eg. "wir" as "viah" instead of "vir"

There may be a lot of accents in England in which people don't pronounce the "r" (although to me it sounds quite normal and correct to not pronounce the "r" in words such as "car" etc) but in some accents of England, the letter "r" is pronounced even when there is no "r" in the word.

In Scouse, for instance, "got a lot of" is pronounced as "gorra lorra".

Well, r vocalisation doesn't mean it's more clear by any means. This exists in German also as I said.