It's a small but important distinction:
The requirement is to provide the source code according to the SSPL's terms, not to relicense to SSPL.
It's just like the GPL but attempts to infect surrounding services.
Any argument against the SSPL's infectiousness can be applied just the same for the regular old GPL, just in a different context.
(Well apart from the elephant in the room: Whether the license can actually work the way it's intended to or not.)