But from paradox's point of view is it preferable to develop and operate an in-game shop as well as all the other in-game online functions themselves or to use a ready-to-go service provided by a third party?
It's better to go themselves, of course. Same as it would be better for Paradox if everyone bought direct from them rather than from
any 3rd party vendor, as vendors all take a cut of the box/ download price while Paradox would get an effective 100% if selling themselves. But including their own store (via Connect, presumably, haven't really checked out HOI: TCG but it uses Connect for paid transactions, IIRC; they could, presumably, have just used a 3rd party there) would potentially be an Origin type situation*, and if they did that wholesale they might not be able to sell on Steam at all. Which is all a bit ironic really, given Steam's propensity for trying to get itself onto every game install possible from whatever source bought.
Is there another game delivery platform that provides all these functions to the extent that steam does?
Patching wise- since that's been cited as a major issue- a huge amount of software has auto patchers. Everything from anti virus, freeware, games, software suites, operating systems, big or small. Paradox's own games have an update button, no great difficulty in making that an automatic check, especially if, as Johan has said, all vendor game versions when installed are exactly the same. It should also be noted that Steam has consistently been far from the most reliable for core Paradox games when it comes to patching (is EU3: DW at version 5.1 on steam even now?) in the past, and for timely releases (DW/ FTM late etc), and for treating the expansions properly (ie forced installs, no rollbacks). I'd quite happily believe that going Steam only would solve
those issues, at least.
Note: I don't have any fundamental problem with Steam on Valve's own games, nor Origin on EA's, nor Impulse for Stardock's and would be happy enough if Connect were enabled in Paradox's software similarly to how the steam integration has been detailed. But I do have an extremely strong objection to forced bundling of 3rd party clients. It's monopolistic and you end up with a closed, console style system just with someone other than MS or Sony making the rules.
*To forestall potential arguments: Gamersgate/ Impulse/ D2D etc have no problem with Origin and you
can buy BF3 at those places, instead of Origin. The only place you
cannot is Steam.