They still would not be nearly as fast. When I'm working with projects consisting of hundreds of files measuring hundreds of lines each, I need an IDE that's capable of using the full performance of my workstation
A counter-argument to this is that all files you need are stored in 'the cloud' and performing searches/indexing/refactoring would happen _faster_ than on your workstation because it can take advantage of a lot more 'cloud' resources.
My work computer is 8 cores, 32gb and a GPU; why do you imagine that a hosted instance somewhere running the web server is going to do a better or faster job than my local computer? Hell, even my laptop is going to do a better job than a cloud server.
Not 'a hosted instance' or 'a cloud server', but many. An arbitrary amount. Personal anecdote: Local full builds for me take 28-30 minutes. When I farm it out to our infrastructure in AWS it takes 9 minutes.
That's true, especially for client-side based online IDEs. At Repl.it we have a hybrid approach where a lot of the IDE-like functions like code intellisense run on the server: https://repl.it/blog/intel