Let's go back to the original university used: Harvard.
Harvard College does not have a degree that can be obtained exclusively online, but one can obtain a bachelors degree from Harvard University by spending only some time on campus.
The University of Maryland really pioneered online schooling (probably because the degree says "University of Maryland" not some wanker name like Phoenix College). They began offering a public university degree in late 1990s and had 15,000 students within 3 years. The credits cost roughly the same.
Since that time, hundreds more universities have adopted either full online or hybrid online/class degrees. We have only two decades to evaluate, but so far there is no universal metric whereby an online program can be disparaged. Further, these degrees do not say "earned online" or "earned partially online", they just say baccalaureatus and they don't materially affect a graduate's prospects.
Perhaps there is a downside, but I would ascribe the tendency to attribute such to the personal bias of the recipient. There is no definitive data that marks them as in any way inferior.
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