Compared to being required to delegate massive amounts of authority to a TTP just to log in to a service that uses non of that authority, it is a simple low impact way to log in. A generic TTP-free signature based login would be great, an I'm not sure, but you could probably just use your memo key for that, but as far as TTP versus micro-transaction goes, micro transactions should be the preferred log-in only option IMO.
A 4th possibility with a TTP that I feel could actually work is a TTP that sells client certificates using memo field in the sell transaction the same way that micro transaction login would.
I'm curious, why do you say that on-chain transactions are the better option for login compared to signing a message with your key proving ownership?
I don't. I'm saying using the blockchain for log-in is preferable to using a TTP for log-in.
In general the blockchain should eventually be able to remove the need for any type of TTP, even for delegation. I think Steemit Inc would do wise to keep close tabs on the Agoric developments and maybe work with Agoric to make STEEM bleading edge with respect to implementing cap patterns for rights and delegations. In the meantime, only using a TTP when delegating, not when logging in, should I think be the first step away from the IMHO outdated concept of TTPs.