Agreed, that was a legendary acquisition.
That being said, I think it was not a mistake for the previous owner(s) to sell at the time. Priceline had cash, and the marketing heavy ("buy ads in January, stay in summer, bill hotel at the end of the month after the stay") business had significant cash flow challenges in terms of growth.
When I joined in late 2010, Booking still seemed to be viewed as a bit of a poorly understood miracle by the group folks, growing nearly 2x every year. Certainly the engineering department was so much less... corporate... than the mothership's that we were sometimes referred to as the cowboys in Amsterdam.
Shortly thereafter, they hired Darren Huston to run Booking, who relatively soon after that (like 24 months? I'm sure Google search will find that answer) also became the group CEO, all based in Amsterdam. At the latest then, Booking would have been officially the core of the company, even though it had been the growth motor for well longer.
Historically, the benefits offered by Priceline group to booking were IMO chiefly aforementioned cash flow for growth, and shared technical infrastructure (WAN, shared colo space). Booking had outgrown the group infrastructure team's ability to scale. The perpetual culture clash eventually led to the central infrastructure group being broken up (very much an outcome driven by the booking CTO, Brendan Bank). So we built our own network and DC team since we had far, far outgrown the infrastructure needs of other group companies.
For a long time, Booking was so focused on only doing things that were strictly measurable and attributable that we didn't do any brand advertising or classical marketing (cf. quantitative fallacy). We co-grew with Google search ads in particular and had built very significant tooling around AdWords since the Google provided infrastructure didn't scale. Unofficially, we were the largest ads customer for a long time spending billions annually at useful ROI.
This "stealth mode" meant that we weren't getting a lot of DDoS type threats to deal with for example and likely less fraud risk. It also meant that we always chuckled in earnings calls when analysts praised the "Priceline business being very successful overseas". Eventually reality caught up and PCLN became BKNG - Booking Holdings.
'twas a wild ride. Not always fun but chock full of learning.
AMA if you like.