If you minify in your build pipeline and gzip in nginx/Apache, everything is faster and more resource efficient. I almost think that even just enabling gzip in nginx already makes it faster. Did you run some benchmarks?
Yes I think I prefer minifying and gzipping as part of the build/deploy phase, as then you only do the work once. I don't use nginx/apache in front of go any more as it's just one more moving part (prefer load balancers), so would be interested in what others are doing in order to serve content gzipped.