1. Evaluate the attached .el file.

2. Start typing, randomly and with certain pauses, trying to align the
interval to the "Contacting host" messages.

At first, Emacs is responsive, and the requests are duly aborted, like
'while-no-input' obliges them to. A little bit later (maybe 10-30
seconds later), I see errors like "Transfer interrupted", and Emacs
stutters when that happens. Later on, any HTTP request to the same host
freezes Emacs until I press C-g. The attached screenshot shows the
messages log and the list of processes at the end.

I guessing this became much easier to trigger with
12e922156c86a26fa4bb2cb9e7d2b3fd639e4707 when eldoc started using
when-no-input. But whatever underlying problem is there in url-http,
it's probably been there longer.

In GNU Emacs 27.0.50 (build 20, x86_64-pc-linux-gnu, GTK+ Version 3.22.30)
  of 2019-03-05 built on zappa
Repository revision: 9b93e3b0759d562989283eaecf32e075f984c18c
Repository branch: master
Windowing system distributor 'The X.Org Foundation', version 11.0.12001000
System Description: Ubuntu 18.04.2 LTS