Other posts have covered that illegal is not "place" assimilation.
The etymological origin of words starting with ill- is irrelevant to the grammar of modern English. Some words may have forms that can be explained only historically and not by synchronic grammar.
But not all negative words starting with ill- date back to Ancient Latin sound changes. For example, the adjective "illiquid" does not seem to exist in Classical Latin; Google shows some uses of "illiquidus" in post-Classical Latin, but it's unclear whether these are plausible sources of the English word.
If present-day English speakers sometimes coin words like "illiquid", which seems likely, that raises the question of how to explain what they're doing when they form these kinds of words (e.g. why is it formed as "illiquid" and not as "inliquid"?).
Also, even though words like illegal and illegitimate do go back historically to Latin forms with ill-, we can ask how English speakers today acquire and mentally represent this kind of vocabulary (presumably they notice that these words are related in form and meaning to legal and legitimate) and why these forms continue to be used rather than being replaced by forms like inlegal or unlegal.
Obviously English does not as a general rule assimilate /nl/ and /nr/ to /ll/ and /rr/. But it is possible to argue that English has a morphophonological rule that causes the /n/ in the specific morphemes "in-" and "con-" to assimilate to a following /l/ or /r/ (with the resulting geminate then being simplified to a single consonant).
Whether it's plausible to postulate that English has this kind of morphophonological process applying to restricted subsets of vocabulary is a different issue. You can find many comparable examples argued for in Chomsky and Halle's The Sound Pattern of English and subsequent work; e.g. things such as "trisyllabic laxing" and "velar softening" have been argued to be rules of English even though it is possible to find surface violations of the rules that these processes follow.