As it shares some of the tracks with the Hanwa line, I'd imagine there is some risk of delays. I don't think it's common for it to be delayed though. I'm not sure about the Kishuji/Airport rapid service though, as a lot of those trains split up/combine with the Hanwa line at Hineno (anyone in south Osaka or Wakayama will tell you the Hanwa line is a complete and total mess!).

I still cannot fathom why Osaka city and the surrounding prefectures didn't lobby through a Shinkansen line extension to KIX? There have been all sorts of crazy infrastructure projects in Japan, this would have been one of lasting effect.

And why not re-introduce check-in facilities at Kyoto station? The service could be limited to premium passengers but at least something could be tried to revive the local economy.

Well, as I said, Haruka shares tracks most of the way; in order, JR Kyoto line, Osaka Loop line, and Hanwa line. Hanwa line gets crazy every once in a while (I use it to go to one of my workplaces), but the line that is most likely to have delays in Haruka's route is the Osaka Loop line. The Kansai Airport/Kishuji rapid splitting at Hineno hasn't led to delays, as far as I heard. It doesn't take that much time to do (JR West does it all the time with some other trains).

The reasons why there is no Shinkansen line to KIX is because there is no place to put the tracks, some areas along the way would have to be reinforced to support the weight, and no community along the way wants to deal with the noise. Shinkansen is meant for long distance travel throughout the islands, not for commuting between an airport and cities.

Reintroduction of check-in at JR Kyoto station and in Osaka City Airport Terminal (OCAT) was considered for a while, but now won't happen because of the new security laws that came into law lately. No Japanese airlines wants to deal with the costs and liabilities.

Yes, I used to use the OCAT check-in facility and it was pretty convenient. HKG still has a check-in facility at Central for the Airport Express customers. Regular Metro customers don't get the privilege.

The loop line is usually fine (I've only had 2 or 3 minute delays and nothing big). I can't say the same about the Hanwa line (which is 6/6 out of delays on the times I took it, including a 90 minute delay in total). The Hanwa line's mess may screw around with the splitting at Hineno because I'm not sure what JR does if the Hanwa line part will be delayed. I didn't bother to pay attention last time I came back from Wakayama (when I had the 90 minute delay, although by that point we were only 70 minutes late)