Life could be so easy without MS

I am using tinydns as DNS server software, which defaults to
a.ns.DOMAIN and configuring spf entries is a bit..uhm

I don't bother running a DNS server and let the registrar do this for
me, but then again I'm only controlling a handful of domains with even
fewer email users.

Sites like requiring registration I do not
like much, as I don't like the idea that (not only a) third party
controls email flow even through hubs.

This service sounds a bit like snake oil to me. I guess if you have a
working postmaster@ address and keep an eye on the mailer log (e.g. via
one of the many log monitors/analysers) then you'll go a long way.

If you want feed-back, have a look at DMARC. This allows you to get
regular summary emails from most big email providers about accepted and
rejected mails from your domain (from your server and from spammers
trying to impersonate your server). But you'll need to post-process the
reports: the reports are too many, in XML format and a pain to read.