Hotels often only issue the invitation for the dates you are staying with them. Which means the visa is also only valid for those dates. Whereas the agencies will give you an invitation whatever dates you ask for (max 28 days or thereabouts).

You can arrive after your visa starts and leave before it ends – so it gives you flexibility if plans need to change at short notice.

BTW – there are delays in processing visas in London at the moment. I went to submit my papers and fingerprints on Tuesday and have been given 13th Feb as earliest date to pick up. (non express service).

I have used Real Russia in the past – this time used https://visatoruss.com/ . Invitation was sent within minutes.