The biggest problem I see with the current system is that a small number of authors venue shop by repeatedly submitting the same paper without changes.
Allowing submissions to happen in parallel will benefit that group of bad actors to the detriment to pretty much everyone else.
Also, all submitting in parallel will do is increase the number of erroneously accepted submissions. For one thing, typical reviewers review for multiple conferences, so you'd just be sending the same manuscript to the same person multiple times. Also, most related conferences have a fairly similar bar.
In fact, most papers have pretty good alignment on reviews. Reviewers typically can't see each other's reviews or discuss the paper before submitting their review, so these are mostly independent samples. There are papers that have bimodal scores, but it's rare, and usually due to low confidence reviews or the very occasional controversial paper.
It is often detected when people just ignore previous reviews, and resubmit without revision. Typically, one reviewer will overlap between the two conferences and notice the resubmission. If the paper hasn't changed, that's an easy reject, even if the person wasn't assigned to review it. Allowing parallel submissions would normalize this class of denial of service attack against reviewers.
Also, far more often, the previous reviewer will take a look, and say that the authors did a good job addressing the previous group's concerns. Of course, that can't happen if the paper is submitted in parallel. Allowing parallel submissions would put people that actually improve their work between submissions at an unfair disadvantage.