For a couple of years back around 1997 - 9 I was Head of Type Approval for all UK maritime radio, radar, navigation aids etc, and a Notified Body in EU-speak. This meant I was fairly heavily involved in rule-making, including stuff like the LV and EMC Directives. TBH, the only really significant flaw with EU rule making was that large manufacturers within the EU had, IMHO, far, far to much influence. Often it seemed that regulations were framed more to protect commercial interests (especially, but not exclusively, those within Germany) than they were to make goods safer, more reliable and more effective.
The vast majority of EU regulation is, not withstanding that criticism, fairly well drafted and sensible. The primary flaws we experience seem to be associated with a peculiarly British tendency to try and follow regulations to the letter, rather than use them as guidance. The French, in particular, never seemed to be able to understand why we would get so vexed about a particularly rigorous and difficult regulatory element. At times there was almost a Gallic shrug, indicating that "the rosbif's are mad, again". Much of the UK annoyance with EU regulation is not with EU regulation at all, but the manner in which we have effectively re-written it into statute law here, We like to make rules even where none really exist, for reasons I've never wholly been clear about.
As far as vehicle TA goes, I doubt anything at all significant will change. We buy a large volume of cars from the EU, so it seems unlikley that we'd adopt different standards. We may choose to tidy up some of the slightly bonkers bits of vehicle approval legislation, but my guess is that, if anything, we would try to tighten up other areas, particularly those surrounding full self driving. Some countries in the EU will be an easier proposition than the UK for FSD, just because their road neoworks are no where near as complex a driving environment.