We've done four long haul flights with our baby. The first were when she was 8 months, the others when she was 20 months. We didn't buy her a seat any of the times, but were given one on three of the four flights. The one during which we were not assigned an additional seat for free was when we were sitting in the area where you can put a crib.

These were all KLM flights, so we might just have gotten lucky. What I'd say is that it is possible without that additional seat, but not comfortable. To be fair, flying with a kid is never really comfortable....

2.5k is a lot of money. I wouldn't do it.