Re. 2009 and 'support from Saleh': I wouldn't describe it that way. I would describe it as 'Saudi university of warfare'. They something like 'went through a high school' back in 1991, learned some lessons but that wasn't enough - yet. They continued buying equipment, but weren't training well enough, didn't care about plenty of things. In 2009-2010 they learned how to organize on their own, how to train, how to fight, what equipment works and what not etc.

What happened during that war was that Saleh launched that Operation 'Scorched Earth' - and had the backsides of his military returned to him by Houthis on a silver plate. The 'Sa'ada Axis' (de-facto a corps-sized unit of some 8-9 brigades) was largely smashed, with some of its best units either overrun or at least besieged by insurgents.

Then the Houthis made a mistake and - I still don't know why - 'invaded' Saudi Arabia. That is: they attacked some border post, and captured a few peaks. What happened next was not related to Saleh's war against Houthis - no matter how much the Saudis declared it as such.

Saudis thought they are so good, that 'rag-tag gang of terrorists' would fold and run away on sight. They rushed a hodgepodge of various units that were nearby - supported by one of para/commando battalions and another of marines. These eagerly assaulted - only to get smashed by insurgents fighting from well-concealed positions (Saudis suffered over 200 KIA in the first few days of that war).

That taught the Saudis to plan their ops, to organize etc. They set up a joint HQ for all branches, deployed all of their means of intelligence gathering, carefully reconnoitred the area and then began smashing Houthis, bit by bit. That took much more time (and was particularly expensive in terms of PGMs), but after a few months of experiencing a sort of an onslaught Houthis never experienced before, they agreed to give up. From their POV, there was no point in continuing to expose themselves to Saudi pounding, if their actual opponent was in Sana'a...

In 2015, Saudi military was better prepared than ever before. But, their political masters fell for Hadi's 'promise' that the Yemeni military would do nothing (especially not side with Houthis) - supposedly because Houthi re-formed that military and purged all the Saleh-loyalists - and that Houthis could be defeated in similar fashion like back in 2010.

That was not a 'bad' but 'stupid' idea. Actually, it's so that there is no way Saudis can force anybody in Yemen to accept their terms any more.

If I am reading you correctly, the Saudis are going to have to have a “come to Jesus” moment and negotiate with Saleh. Yet Saleh is divisive and excels more at playing spoiler and rendering Yemen ungovernable without his imprimatur, than he does at governing without unrest. But Riyadh will have to make hard choices and prioritize.
Yes and no.

One of things I think one should consider about this war is that various 'assessments' and 'estimates' about the composition of the local population usually published in the West (or at least in English language) are simply BS. Somebody there is implanting entirely wrong data in this regards.

Namely... sure, there's no doubt that Saleh is a master in political intrigue and maintaining himself either in power or in a position of influence. And, there's no doubt that over the time he cooperated with nearly every political entity there can be in Yemen (including AQAP, Islah, all sorts of tribes and whoever else). But, that's still no explanation how comes that he - as a Zaidi - won two ('quite fair', even if 'not perfect') elections by quite a wide margin. I don't think this would be possible if Zaidis make 'only' about 30-40% of the Yemeni population, as usually explained.

Now comes the particularly 'problematic to explain' part. Namely, Saleh managed to win elections 'although' he was at odds with Houthis, who are Zaidis too. And although the Houthis have destroyed large parts of various tribal federations - including several of particularly powerful and famous ones - over the last 6-8 years.

That's why I do not find the usual explanations about 'secret of his success' being something like Saleh's ability to convince various Shafi (Sunni) tribes and the Islah Party to cooperate with him, and why I'm not convinced usual publications about the composition of Yemeni population are correct.

Anyway... the Saudi-led military intervention had an additional effect of turning additional parts of Yemeni population against Saudis (and allies, including the USA). Sure, you'll not get to hear a lot about this in English-language. Reason is that English is spoken and social media used by those Yemenis that can afford such luxury. Most of these are (relatively wealthy) businessmen, who were against Houthis and Saleh all the time. But, they are few in numbers - especially in comparison to masses of impoverished Yemenis, most of whom are meanwhile on the side of Houthi/Saleh.

All of which means: even if Houthis would withdraw from Sana'a literally within the next 5 minutes - which is the core demand of Hadi, Saudis & Co KG GesmbH AG SPA - there is absolutely no guarantee anybody could install a new Hadi government there again (indeed: I wouldn't bet 5 bucks on Hadi surviving his 'return' to Sana'a, just for the start).

Is confronting Saleh’s coup d’état worth Iran gaining a foothold on the Saudi-Yemeni border?
There was no 'coup' as such by Saleh. He simply sided with Houthis, and this resulted in about 60% of the military following in fashion.

Iran had absolutely nothing to do with this. In total context of this war, the few IRGC/Hezbollah advisors that did train something like two battalions of Ansar Allah - and thus any kind of 'Iranian involvement' - are actually not worth mentioning. Despite all sorts of Saudi and IRGC's PRBS, Houthis are anything but 'Iranian proxies'. I really recommend dropping that thought completely to anybody who wants to understand this war.

What would make Iran find the intervention in Syria costly? Obviously Johnson’s idea of cost differed from Minh’s in the 1960s…
I do not really like to compare different conflicts, but I might make an exception in this case. If there is any experience from the Iran-Iraq War, then the one that the IRGC has no problem with 'endless wars'. Although anything but suicidal - as often, and entirely wrongly described - the IRGC can't care less about losses (on the contrary: the more martyrs the better; it does not care the least about such issues like costs, economic or material damage; it does not care about enemy's superiority in arms and firepower etc. Means, one can't defeat it in classic sense, like through a war of attrition etc. Only though a synergy of multiple effects, a combination of all of them.

That means: one would not only have to defeat it on the battlefield; not only have to cause devastating losses in order to demoralize it; but this would have to be combined with a complete isolation of the country on the international plan, severe damage to the Iranian economy (like through air or missile strikes), and demoralization 'at home', in Iran.

As for Israel, I think it is satisfied that the Sunnis and Shias are killing each other and not fighting the Jewish State.
Sure. But a very short-sighted policy too.