I honestly view this point - that there were prior waves of immigration from various European nations, and before that concurrent waves of forced migration from Africa and elsewhere (though this is left unsaid) - as a bit of a non-sequitur, bordering on bait, largely because it happened over a very long timescale into an essentially empty nation. Suppose I answered in the negative (that I don't think there was anything wrong with it). That wouldn't change anything at all about the current debate. It isn't some kind of gotcha, that if I don't have a problem with British/Italian/Irish/German/French/whoever coming during various migration waves it somehow neuters any particular point about how
any immigration regime should, in my view, be structured such that there are clear and defined benefits to the people
already living in the country. Enumerated elsewhere in the thread, but the H-1B system in particular is for the benefit of
industry (POSIWID etc etc). Not people already here.
It is worth noting, though, that after the peak of immigration in the late 19th century and ending in the 1910s, the United States very intentionally shut off immigration to allow time for assimilation to do its work.