We deliberately don't use type=url because we want to allow people to enter schemeless URLs (e.g.
www.example.com) and default the https:// scheme in this case for easier typing of URLs. I find type=url overly restrictive because of this.
We could use inputmode=url though as it doesn't enforce this AFAIK and just provides the appropriate keyboard layout. One downside that I am aware of for this is that on iOS it hides the spacebar (makes sense as URLs can't contain spaces), but this makes editing the URL more difficult as that's useful to move the cursor (but pressing and holding on the space bar and then moving the cursor left and right). Personally I use this a lot and get annoyed when sites use inputmode=url, but maybe that's just me and the gains of dots, slashes and .com buttons are worth that trade off? Or maybe it's just bad design on iOS's part?
Curious to hear yours (and others!) thoughts on this.