Every variant has come from some poor undervaxxed country so far.
Unless I'm reading this wrong, you seem to be implying that "every variant" arose due (at least in part) to vaccines not being distributed quickly enough to poor countries.
I do not see how this could be factually correct. Omicron is the only variant of concern (VOC) that was identified after vaccines were first introduced anywhere (other than trials). Restated, every country on the planet was "undervaxxed" in 2020 when Alpha, Beta, Gamma, and Delta were first identified:
Omicron is the only VOC that was not detected in 2020.
Here are the dates for the two VOI's:
All viruses, including SARS-CoV-2, the virus that causes COVID-19, change over time. Most changes have little to no impact on the virus’ properties. However, some changes may affect the virus’s properties, such as how easily it spreads, the associated disease severity, or the performance of...
www.who.int
Mu is the latest (January 2021), but this is still well before vaccines were widely available anywhere.
The very first vaccinations in the US and the UK were in December of 2020:
The very first Pfizer jab in the UK was on
12/8/20:
Margaret Keenan, who turns 91 next week, becomes the first person in the world to get the jab as part of a mass vaccination programme, calling it the "best early birthday present".
www.bbc.com
The first AZ jab in the UK was on
1/4/21:
The PM says the number of vaccine doses will amount to "tens of millions" by the end of March.
www.bbc.com
The first Moderna jab in the UK was April of 2021:
The vaccine is the third to be used in the UK, with England's rollout due "in the next few days".
www.bbc.com
The first Pfizer shot in the U.S. was
12/14/20:
https://www.nytimes.com/2020/12/14/nyregion/us-covid-vaccine-first-sandra-lindsay.html
I'm not sure when the first Moderna shot was administered in the U.S., but the Moderna vaccine was approved by the FDA a week
after the Pfizer vaccine:
Two RNA vaccines will be useful as US infections surge, but the speedy authorizations complicate clinical trials.
www.nature.com
The first J&J shots in the U.S. were given in March of 2021:
The long-awaited, one-dose Johnson & Johnson Covid-19 vaccine has now been administered in the United States for the first time outside of a clinical trial.
www.cnn.com
The AZ trial in South Africa was halted because it was (apparently) not effective against beta, which was already circulating there in early 2021:
>>>Another COVID-19 vaccine has run into trouble in South Africa, showing less protection there than elsewhere because a SARS-CoV-2 variant that can apparently dodge key antibodies has become widespread. In the wake of the new finding, the country halted plans to next week to launch the country's first immunization campaign with the vaccine and may instead switch to a different one. . . . COVID-19 vaccines made by
Johnson & Johnson (J&J) and
Novavax have also been shown to offer weaker protection against B.1.351 [beta] (also known as 501.V2), the SARS-CoV-2 variant that now causes the vast majority of all infections in South Africa, than against older variants.<<<
www.science.org
According to wiki, India started vaccinating people on January 16, 2021 and 85% of the eligible population has received at least one shot, and 60% of the eligible population is fully vaccinated (this compares to 74% and 62% in the U.S.).
en.wikipedia.org
I mention India as an example of a country that has actually done quite well with it's vaccination program.
It is true (according to the ourworldindata website) that "Only 8.5% of people in low-income countries have received at least one dose"
Explore data on COVID-19 vaccinations across the world.
ourworldindata.org
Having said that, I've seen no evidence that the VOC's to date came from these countries and that it would have been possible to prevent the VOCs if there had been even more heroic efforts to distribute vaccines around the world at the instant the vaccines started to become available.
It's hard to see how it could have been possible to vaccinate the entire planet prior to the end of 2020 (i.e. before Alpha, Beta, Gamma, and Delta were first identified). It's possible these variants had been circulating for some time before they were identified. This makes it even more implausible to think it would have been possible to avoid these variants by distributing vaccines around the world.
Going forward, who knows?