Because they know that 10-20% of the total sales can still be profitable, especially the smart ones like Yamaha, Onkyo and Marantz, who managed to keep the cost down by adapting their AVPs from their AVRs, much more so Yamaha because they only skip the power amp section and the balanced connections, keeping everything else mostly the same.
I think that's the other main reasons, somewhat we respect the brands that also make AVPs, just look at D+M, how come people now think Marantz is the high end brand of D+M, when in reality the opposite should be true based on the two companies history, who made the world's fully balanced AVP first, and turntables, cartridges, exotic integrated amps, its Denon!, but they decided to keep Marantz AVP so people's perception changed, though it was rooted by the small group of audiophiles who belief in Marantz's marketing warm sound did come from the old days so they had the base to begin with and that helped.
Me too, but that's because I don't mind spending more, and always (and still do) like all kinds of power amps, if I were to downside, I would most certainly sell everything and then pick up an AVR for my old age enjoyment.
For the new comers, if on a budget, I think it is a good way to start by investing on a midrange AVR such as the RX-A6A, AVR-X3800H, Cinema 50, Onkyo RZ30, kind of deal and add a 3 channel poweramp like buckeyeamps and they will get 90% of the performance of a top notch AVP+multichannel power amp, based on the popular 5.1.4 or 7.1.4 setup. Just forget about the presumed longer life of AVPs in that case, instead, just prepare for an upgrade every 5-7 years.
Absolutely, it is less about sound quality and reliability, but the feeling.
That's the reason I just got two Bryston 9B-cubed. Although I still love the Yamaha MX-A5000 11Ch amp, I love the Bryston amps more.