And this is a problem. Lowest-bidder-wins always creates a race to the bottom.

At least in the province of Venice, there was a complicated set of rules to pick between bidders of public contractors - so the law is certainly not universal in this regard.

If I recall correctly, it was based on percentiles instead of taking just the lowest bidder in an attempt to avoid companies racing to the bottom.

This in turn created a system where winning ad these bids was mostly by chance, and unsurprisingly was found to be rigged several times. But I digress...

I think the actual (EU) law is closer to "best suited". You have a number of offers to select from and have to say why you chose that offer. Saying "I chose them because they were the cheapest" is the easiest and safest solution so that's what usually happens, but it's not the only option.

You have to pre-declare how you choose the best offer. Final procurement order is oftentimes made into existence after many rounds of rejection by procurement overseeing committee.

Not quite, but they have to justify the choice to use a service that costs more.