eBay had it's own P2P payment system too. It lost to PayPal, because PayPal was superior at many things (eg. marketing), but also because they cracked the fraud problem (which was an existential crisis early on in their history). I recommend reading the book "PayPal Wars" for a better historical accounting.
True, but that was all very early. The Paypal acquisition happened in 2002. "Success" in the P2P space in the late 90's/early 2000's was at a much, much, smaller scale.
You said: "...Paypal being the default payment..." I'm saying: They didn't just get anointed as the default by eBay; they became the default (and survived this long!) by taking an aggressive stance on fraud and risk.
Also... the scale wasn't as small as you think. According to the numbers [1], PayPal was doing >$2B in transactions at the time of acquisition. For perspective, estimates from 2014 [2] put Stripe at $1.5B in transactions (and a company valuation of $1.75B). Paypal wasn't small, even in 2002.
