While I agree that it would be need for Archer!Herakles to be summoned, he's probably in the category of "too powerful to maintain story drama" for Chaldea to summon this early in the story. Which sucks, because Artoria Pendragon would be a phenomenal Servant for Taylor, creating a very interesting character dynamic between the two and adding to the hilarity of Emiya trying to deal with that situation.
I know double posting is frowned upon, but I had more to say than I thought and it's been a few hours. Essentially, I don't think archer heracles is too strong. He's strong, or he should be, probably one of the strongest Servants, but this chaldea already has Servants like emiya and aífe, both of which are ridiculously powerful, though emiya hasn't shown to what extent.
Additionally, we've also seem Fawkes add or change things to make objectives more difficult, either by adding more Servants, changing abilities, or elaborating on circumstances(like we see with the anne vs the hind)
In essence, there are ways to increase difficulty in natural ways. Off the top of my head, if fawkes gives chaldea even stronger Servants they could have it so the heavenly bull Ishtar lost was corrupted by tiamats sea. Though it's not perfect, she did loose it and it would explain why its gone.
Though that us easier said then done, upping difficulty that is.
Another problem would be Archer heracles stats, but thanks to strange fake we do know some.
We know he'd have god hand, nine lives, the bow of Hydra and the pelt of the Divine beast.
Godhand is a given for heracles in all his classes. Nine Lives is straight up said to be accessible in all but Berserker. The bow if Hydra is heracles bow in general, and is something the wiki does say he has, and we know heracles has the pelt of the Divine beast/nemean Lion as in fakes manga we see it tied around his waist and after becoming alcides, he pulls it off and uses it as a shroud, so we see it in both forms.
This is however entirely speculation, though speculation I'm fairly confident in. We can also say that heracles archers strength is probably A+ as we see it for both alcides and Heracles berserker. But this is more uncertain.
Either way, easier said then done. Point is, I have full confidence that if fawkes wanted to/planned to, they very well could.