I don't AFO is Deku's father. It wouldn't add much to the story. He already sees All Might as his mentor/father figure. There's no conflict.
Of course it'd add to the story. In fact it'd add quite a bit to Deku's character because he's currently boring as fuck.
There's at least two elements that make me think this theory could be true: AfO and Deku sharing the same doctor and the recent chapter where Bakugo straight up compares Deku and AfO.
Now one important thing to keep in mind is a good story doesn't introduce narrative threads if it doesn't intend to do anything with them. Which means that there's a reason why a character establishes a link between AfO and child Deku, and there's also a reason why Deku having access to multiple quirks was explicitely compared to AfO's power. These things aren't mere coincidences and will be explored in the future if Hori isn't a completely inept writer.
Now it's true that it doesn't necessarily points towards Deku being AfO's son. There could be other explanations, but I find them less convincing. The doc could have lied about Deku being quirkless which means AfO stole Deku's quirk because he found it valuable. I don't see what this adds to the narrative though: Deku learning he had a quirk all along doesn't seem to be a very interesting development. What kind of conflict is it supposed to create? Deku wanting revenge on AfO? Seems pretty lame.
Now remember what I said about Deku being compared to AfO because you've got a potentially interesting conflict here. If you look at the chapter again it's not a simple passing comparison, the whole thing has an ominous feel to it. It clearly already weighs on Deku's mind. Imagine what kind of psychological effect the reveal would have on Deku, not just the fact his father is a legendary criminal, but how his unique power is the result of his ancestry. It directly ties into the theme of identity that's so prevalent in the story and clearly parallels Todoroki's struggle with accepting his origins. It's not an accident if Deku repeats that he'll make this power his own after worryingly reflecting on the similarity with AfO's abilities. It could be a pretty big crisis for Deku and arguably his biggest hurdle to overcome.
Finally, and even if it's not exactly an argument in favor of the theory, this whole thing reminds me of one of the many trainwrecks from the Naruto fandom. I'm an oldfag now and I was already online 10 years ago when one of the most debated plot points was Naruto being the son of the Fourth Hokage. Evidence for the theory was pretty flimsy and plenty of people were very hostile towards it and thought it was nonsensical, but it ended up being true and it seemed obvious after the fact. I wouldn't be suprised if history repeated itself.