If every state had its own FDA, it'd be as hard for a restaurant / fast food chain, a brand of groceries, etc. to start selling in a new state as for them to start selling in a new country. Same with drug manufacturing.
If every state had its own immigration standards, you'd have to have border checkpoints between states as you do between countries. Even, e.g., Canada and the US have serious border checkpoints. Apart from the inconvenience, it would kill the economy of cities on state borders. (Imagine people from New Jersey commuting into work in Manhattan!)
If every state had its own DMV, you wouldn't necessarily be able to drive between all states.
Every state definitely does have its own DMV, with its own regulations (for instance: some states have Graduated Drivers License programs for teenagers).
The situation with interstate recognition of licenses is interesting: neither the full faith and credit clause nor the dormant commerce clause actually require states to recognize each other's drivers licenses, and in fact many don't recognize each other's learners permits.
There's lots of effort to harmonize laws across states. No reason that Minnesota would do much other than rubber stamp a drug approved in Wisconsin (assuming Wisconsin was not famously bad at approving drugs).
Also, is your last paragraph sarcasm? Every state does have its own vehicle regulations. The feds use project funding as a carrot to get states to do things, but the regulation is mostly at the state level.
Customs, water rights, environmental protections, trade agreements, equal rights, bill of rights, sanitation, the medicine, education, wine, public order, irrigation, roads, the fresh-water system, and public health...
It's not perfect, no. But the 1965 act is specifically the part that protects voting rights of minorities. Would voting be better without that? Especially given that one party has turned voter suppression into an integral part of their strategy for winning elections?
If it were left up to states, a large portion of them would deliberately not have these rules. And the nonstandardization of rules across the other states would mean that even in cases where they existed, the laws and associated court precedents would be a gigantic mess, making it a lot harder to litigate cases.
For reference on situations where minority voting rights are still a problem:
