Climbers & their money do tons for the Sherpas and their communities - but that exchange is at gunpoint: Risk your lives for us, or your wives and children go without food & medicine. It's a no-win situation for them, and it's precisely because it's a no-win situation for them that this is morally fraught.
First of all, keep in mind that many of the alternatives - like going to build the 2022 World Cup stadium in Qatar - are also dangerous. Even the safe ones involve spending your life in a foreign country away from your family (often including your wife and kids), & having to learn a completely new language. For a lot of Sherpas, that's not even an option, since they're needed in their village for the crop seasons. At best, they have a set of ugly options to pick from.
Secondly, telling someone who has no financial security "I'll pay you to risk your life for me" is very different from telling someone who has money. The US military recruits heavily from the poor - and in fact that might be one of the most significant factors (http://surface.syr.edu/cgi/viewcontent.cgi?article=1002&cont...). Is it fair that simply because someone was born into a lower standing, they have fewer options to live a safe life? The morality of that question alters drastically when you offer universal basic income.
As for moving to the US... that's also just not a possibility for 99% of Sherpas. Literacy & education rates are low, therefore so is knowledge about the visa systems (the main one they'd be eligible for is the diversity visa, which is a long-shot lottery anyway), not to mention the obvious language barrier. By design, immigration could only work out for a fraction of the population. Plus, a lot of them probably don't want to leave their family and culture behind. There's maybe 10,000 Nepalese in the US, and most of them from Kathmandu or the southern areas, which are culturally pretty different.