Well, the experts over at Wikipedia suggest the White House architect Hoban "was influenced by the elliptical chamber at Castle Coole in County Fermanagh, Northern Ireland. That room has identical dimensions, and includes the two recessed niches found in Hoban's original design for the Blue Room." and was designed/constructed around the same time period as Hoban's house.
This all was occurring around the same time, and considering back then there weren't too many houses of such wealth (even in Philly) that could undergo such a fashion statement- after all a bow window is a fashion statement- theres not much practicality there to make it a functional decision.
It was in vogue at the time.
And though President Washington might have taken advantage of the grand window area to greet visiting guests, could one attribute the design to him, like the design decisions he made at Mt Vernon ?
It would be interesting if one were able to prove Washington himself designed an oval tent, then instructed his landlord to add an oval bay window to his house for consistency, further instructing Hoban to add an oval office to the White House to cement his vision forever.
The whole point of this (for me at least) is that American history is steeped in fictional half-truths, and today we are a little bit smarter about things like that. About things like slavery. Its all complicated and theres little black/white but mostly grey.
and then, again, from wikipedia because I ain't no historian:
Dissatisfied with the size and layout of the West Wing, President Franklin D. Roosevelt engaged a staff architect, Eric Gugler, to redesign it in 1933. The modern Oval Office was built at the West Wing's southeast corner, offering FDR, who was physically disabled and used a wheelchair, more privacy and easier access to the residence.