Are asyndeton sentences run-on sentences?

it is a fine line between asyndeton and run-on sentences. I suspect that you would be better served by making a series of sentences rather than linking all into one sentence, with or without using conjunctions. we may speak (in practice) in the way that you are attempting to write, but it tends not to work well when actually written.

Writing is not speaking, yet we often try to write in the same form and structure that we use when speaking. That often does not lead to easily read material.

Standard English requires a ",and" or ",but" or ",or" between two independent clauses. If you are using just a comma or leaving out the comma and the conjunction, you are using run-ons, which are errors in standard English. There is no way to use a run-on and be correct.