I started exclusively using TypeScript in all of my new projects starting a few months ago and haven't wanted to look back since. I always set the strict flag to ensure I get the most type checking possible. It is true that this makes things a... pain sometimes (and I will occasionally find myself reaching for the easy way out of using "any") but I find it helpful much more often than not.
You also can use something like ts-node to run your serverside code. Yes, it has to initially compile things before starting but then I believe the result is cached - for a long running server I don't think this is an issue but start times for something like a lambda function could be problematic. Even in this case, all you need to do is compile your typescript and run the bundle.
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