As I said, it is an odd option - but being part of Britain, and Britain refusing to defend it is far more politically contentious at home then doing so with an ally.
They cut Hanover loose at least in part because they couldn't defend it properly, despite it being the ancestral home of their ruling family. And that was defensive fighting on their doorstep, not an aggressive war halfway across the world, which is what you'd need to retrench the Persians in the Caucasus as you suggested. I don't think British political considerations are the main stumbling block here. You certainly aren't kidding about it being an odd option, though - can you name an OTL instance of a country becoming a protectorate for
offensive purposes? I might be able to myself, but off the top of my head, I've got nothing. And while I'm no military expert, my political instincts tell me that the weirder and more complicated an arrangement is, the more desperate and unlikely to work it is.
England has easily the largest population in the area, and given time to build infrastructure between India and Persia (i.e. Khyber Pass railways, etc) - Russia simply cannot apply the same number of troops to the region. I admit "Winning the Great Game" is nebulous, but I'd call it. Russia might still get some stuff, but overall, Britain has won there.
That's already OTL, since you must count India for this to actually be true. I'm not convinced it makes a difference. For one, the infrastructure improvements would be quite expensive, and compete for funds with similar projects in India proper. Roberts was appalled at the state of Indian roads and rail. I doubt he'd be any happier about the need to spread that money even further.
And about the troop numbers. The most sophisticated analysis of the Russian threat to India from this (general) period was MacGregor's, and he estimated that the Russians could encircle the Indian frontiers with just shy of 100,000 troops. That's a significant fight to begin with, but extending the sphere of British influence into Persia may actually allow the Russians to bring even more bodies to bear. That extra commitment puts even more pressure on the Indian army that's already about to mutiny. I'm pretty sure the British were never in real danger of losing a defensive war for India, but expanding into the Caucasus or Turkestan seems like a bridge too far. And if they're unwilling to do the former, then again, the Persians lose their incentive to go through with this.
Lastly, there's the politics. Every time Russia expanded further into Central Asia post-Crimea, they scrambled their diplomats to assure everyone that their move was temporary, that they had no designs on India, and that nobody should worry about it. The British complained at each of these moves nevertheless, and the incongruity between the Russian Foreign Ministry's pronouncements and what soldiers did on the ground. One big albatross the British had were accusations of hypocrisy - how could they whine about Russian invasions of Bukhara or Khokand, when they themselves had not too long ago invaded Afghanistan, as well as annexing Sindh and the Punjab? Adding Persia to this collection makes the political situation even more fraught, and far from a deterrent, could easily prompt even more aggressive action from the Tsars, as well as providing the political cover to do it. Far from settling affairs in Central Asia, it risks intensifying the OTL competition, is certain to increase costs in this quarter, and will face periodic disruption based on events in London, because the Liberals hated this kind of forward policymaking in India.
So without a serious effort at reclaiming Persian losses to the Russians, this is a risky and expensive boondoggle. If that effort is made, then it starts the war that most India hands wanted to prevent.
I don't think that is a fair assessment - the point is that its a trade - Herat, and support, in exchange for 'insert arrangement details here'. There is no strong-arming of them by the British, the point is that this is a deal that Iran proposes. They aren't meekly bowing, they're essentially recognising that they aren't equal, but not being meekly submitting.
The point remains that it's a recognition of limited options and limited influence. They certainly can't expect it to result in Britain ponying up on a commitment they'd shirked twice before (the Caucasus thing). And given the tenor of their relations at this point, it'd also be unusual for them to expect this to result in an acquiescence on Herat.
In fact, if you compared it to a feudal vassal, Iran asking for Herat in exchange for fealty is pretty standard. Compare the two outcomes - A large client state, or a small independent state that you'll have to prop up. One is clearly more advantageous than the other.Heck, it wouldn't surprise me if the deal goes somewhere along the lines of a Anglo-Iranian garrison in Herat for at least 10 years before it is handed over to Iran to garrison on its own, because it is so unexpected.
Actually, the other likely outcome is OTL - Herat being claimed by Dost Mohammed, the other British ally in the region. Relative to the Shah, he was a better-known quantity, having been befriended by British agents as well as his own captors during the Anglo-Afghan War. Despite having fought him before (which is also true of the Shah), they had a good rapport and a good read on him. And seeing as the Khyber Pass bordered Afghanistan, not Persia, retaining that friendship was far more important from India's standpoint.