I asked a native speaker and the following are his responses representing his theory, edited slightly (posting here with permission). N.B. He emphasises many times that this is speculation. Also, Arabizi is used for the Latin transliteration, so "3" represents ع.
I can't really give you an educated answer that's backed by any resources, but I can give you my theory.
It has to do with syllables and the word ending with an alif mamduda ا. Take the word طبعًا as an example; "tab-3an", it's two 'complete' syllables where each one has two non-vowels and a vowel separating them. Both the syllables are 'mirrored' in a sense and removing any part of the syllable will make the word feel incomplete (kind of skewed) such as "tab-3a". Same can be said for أهلًا, "aah-lan". Saying "aah-la" makes [it] seem like there's something missing in the second syllable. That's why you really only see أهلًا pronounced without the tanween if it's followed by something, like the common saying "ahla w sahla" أهلا وسهلا. If you divide the whole sentence into syllables, you'll see that the و is filling in that empty spot "ah-law sah-la". You might ask why سهلا didn't get a tanween, and my answer would be because the whole sentence seems complete. It goes xx-xxx xxx-xx, as in it's completely mirrored.
I also want to mention that the syllable formula of xxx-xx is very odd for Arabic. Even in MSA [Modern Standard Arabic]. I can't really think of a word that follows this sense of syllables.
Now jumping into مرحبًا, you'll notice that it's a special case in which it doesn't have two syllables like the others, but rather has three. "mar-ha-ba". This is actually a very common syllable formula in Arabic, and thus sounds natural with the tanween or not. Similar words share this formula such as مَرْكَبَة "mar-ka-ba", مِدْفَعَة "mid-fa-3a". That's likely why this was an exception!
[T]ake [this explanation] with a huge grain of salt, but syllables in Arabic formulation matter A LOT. If you ever get into Arabic poetry, you'll notice that a lot of them balance out the syllables in either side and usually follow a specific pattern as to not have one that's out of place or the sense that one is missing