I've answered this question in depth before. My first answer on r/AskHistorians was actually a variation of this question and it's still the most popularly asked question regarding the history of Tibet.

'disgusting how the liberal left embraced the Dalai Lama when he was more or less a theocratic dictator in Tibet,' implying vaguely that perhaps the Chinese annexation of Tibet was a good deed.

This is a good alarm system you have going. Statements like this are usually accompanied with justifications for the Chinese activities from the '50s to today... glossing over the way the People's Republic (often violently, and always forcefully) dismantled the Tibetan society, often by packing the committees and government bodies that actually did any governing with Han Chinese and Party cadres, while placing Tibetans in figurehead positions (they did this with the Dalai Lama himself from roughly '56 on) as evidence that Tibet was a willing partner in their "liberation."

Statements like this imply that the Chinese "liberation" solved all of Tibet's problems and established a modern functioning society without slavery and imperialism (accomplished by Marxist-Maoist ideology which simply states that imperialism and slavery are simply "impossible" under Communism, therefore under a Communist regime, by definition there is no slavery or imperialism...). And then completely ignore the forced collectivization of the '50s and '60s, the involuntary seizure of cultural artifacts, the thousands of tonnes of gold stolen from Tibetan monasteries which was sent to Beijing, melted down into gold bars, (and then mysterious, the PRC paid off all of its debt to the Soviet Union in 1965. Weird timing, huh?).

Even today there is a lot of problems between Tibet and China and any consideration or balance is usually taken as a form of dissent which makes discussion on this topic very difficult. It's easy to see why: both Tibetans and Chinese have faced centuries of discrimination (religious and ethnic) at the hands of outsiders and are defensive about their history. Rightly so. Though Tibet was certainly not a "Shangri-La" that westerners (and Tibetans themselves) often portray it. Nor was Post-Liberation Tibet suddenly a happy place where poor Tibetans were lifted up by Communist brethren (as Chinese propaganda portrays it).

Would a rule for Tibet under the Dalai Lamas have been 'good?'

This is a fundamentally impossible question to answer. Most Tibetans will answer "yes," and most Chinese will answer "no," for reasons stated above.

Tibet from 1912 - 1950 was in a period of state-building. The Thirteenth Dalai Lama (the current one's predecessor) was trying to build Tibet into a modern, independent state. And that necessarily involved developing the country, modernizing the military, cracking down on the tax code, and then suppressing dissent.

This process isn't unique to Tibet, and is in fact something we can trace through primary source documents in any society and country that has made it from a medieval period ruled by an upperclass religious-based elite, to modern statehood. Even Bhutan has gone through this process, and one of the explanations of the nastiness that happened in the early '60s and the early '90s is a part of the state-building process. India is arguably still going through this process.

State building is, again, arguably, good for many at the expense of the few because it often necessitates modern medicine, modern infrastructure, modern social institutions, and increased civil liberties compared to medieval societies where the concept doesn't exist (though this last point is increasingly being challenged).

Would the Dalai Lamas' rule have been liberal, focused on education, given opportunities for capitalism and fair and free markets for wealth generation, free migration within the country and free speech (excluding lese majeste I suppose).

Again, this is impossible to answer and it's impossible to speculate about alternate history scenarios (not least of which because it is against the rules of this sub.

BUT, what we can answer definitively is that the young Fourteenth Dalai Lama was very pro-modernity and even pro-Marxist. The Dalai Lama has said quite often that he believes Buddhism is the answer to people's Spiritual Needs while Marxism can be the answer to their Material Needs. He and the Panchen Lama went and visited Mao in Beijing in 1954. When the Dalai Lama returned to Tibet (he would stay there until 1959) he was excited that Mao seemed willing to work with and respect the Tibetan's wishes for a slow transition to socialism as opposed to rapid developments.

The PRC had actually told the Tibetans several times during their "liberation," that they had come to liberate the Tibetans from feudalism and serfdom. And once they were liberated, they would not stay "even if you begged us to." Obviously, that's not how it worked out. And the increasingly heavy hand of Chinese rule eventually convinced the Dalai Lama and those closest to him to fear for his life, so he fled to India. Even in exile, Beijing still believed it was possible to work with the Dalai Lama, who has certainly changed in exile: becoming pro-democracy, pro-education, pro-science, etc. etc. How many of these opinions were formed in Tibet and how many in exile? Hard to say. He has dozens of books out, his autobiography Freedom in Exile and the many essays and publications on his website (take careful note of the dates) are good indications of the opinions he held and when.

It actually wasn't until the 1980s and '90s that Beijing formally turned against the Dalai Lama and stopped trying to court the exile administration in Dharamsala. They wanted to try and get His Holiness back to Tibet to legitimate their rule, but after a few short visits of his brothers to Tibet that ended in a publicity disaster (especially for PRC relations with Taiwan) Beijing decided to stop portraying the Dalai Lama as a loyal, but misguided Communist, and start publicly calling him a "splittist" despite the fact that the Dalai Lama has consistently, since 1950, advocated a "Middle Way" approach to union with China: where Tibet was able to manage its own affairs underneath a Chinese government that would manage Tibet's international affairs.

Is there historical precedence for this?

I would say yes: Bhutan is a good example, and of extreme interest to me, because it's the only example we have of a Tibetic culture zone that has been able to function and develop with minimal outside interference.

One comment you often see, esp. here on Reddit, but in any article about the Dalai Lama or Tibet with comments open, is that the Lamas "want their slaves back." Though (as you can see from my original comment in the link above) "slavery" and "serfdom" aren't the same in English language, and they are very different institutions in Tibetan history as well.

Not only that, but Bhutan banned both practices in the early '50s, and then even allocated royal land to the newly freed Drap and Zap so they could move away from their former masters and not feel awkward about the situation.

It's impossible to note when an independent Tibet would have done something similar and made those institutions illegal, again because that's alternate history and it's impossible to know, but it's important to note that every other country in the world has criminalized slavery and approximately 0 of them have needed the People's Liberation Army to do so.

Sources:

Tibet: A History by Sam Van Schaik

Tibet: A Political History by W.D. Tsepon Shakapba

Dragon in the Land of Snows by Tsering Shakya

Tibetan Nation by W. Smith