What are the negative effects to the first author when adding coauthors?

I think for some people, the principle is important: they didn't feel that the person whose name has been added contributed enough, and humans hate the feeling of giving up something unfairly.

That said, there is a very real cost in terms of credit. This will not be consistent across different people looking at your record, but every new co-author decreases the chance that the important part of the work will be attributed to you. There was actually a recent study about this which found that women pay an especially large price on this score: when they do joint work with men, the evidence suggests the men tend to get the credit (the actual observation of the study is that their chance of getting tenure do not improve). You'll note though, even for men a solo paper improves chances of tenure by more than a jointly authored paper with anyone.

Following the link to the Alpher-Bethe-Gamow paper I found that there is an answer for this particular case that seems important. From the Wikipedia page:

He [Alpher] felt that the inclusion of another eminent physicist would overshadow his personal contribution to this work and prevent him from receiving proper recognition for such an important discovery.

For this paper is seems save to assume that many people will consider that the order of the authors has not been decided by contribution. I am not sure about the rules for author order in physics at that time but for sure people would immediately get the intended pun. Hence, I can understand Alpher's concern.

So in fields where order of the authors is not by contribution (or for special paper like this one), having one more big shot in the list of authors may really lead to the wrong perception. In fact, for PhD students in math is in not at all unusual to have papers written directly under the supervision of the advisor appearing with only the PhD student's name on it, even if the supervisor may have contributed some ideas. In this way it is ensured that the work will be perceived as the PhD student's work.