See, the thing is... Sony would have to do a hybrid hardware/software approach to make backwards compatibility. I mean they cannot simply emulate the PS3 on the PS4. Despite the fact that the PS4 is a powerful machine... the unique architecture of the PS3 makes emulating it an absolute nightmare.
For simple understanding the PS3 has a 3.2 Ghz main core with 7 mini-cores (that also operate at 3.2 Ghz) that feed the main core. The PS4 on the other hand has simply 8 cores at ~1.6 Ghz. So both, essentially, have 8 cores.
Which, hopefully, you can already see the main problem.
For those that can't... Emulating a 3.2 Ghz core with a 1.6 Ghz core is not going to end well. Fact is for pure software emulation you need a speed several orders of magnitude better. It takes a 3000 Mhz or higher (3000 Mhz = 3 Ghz) to emulate a PS2... which has a 333 Mhz processor. So you need basically 10 times more power to software emulate it. The PS4 simply cannot do that in this case.
Therefore, what would have to happen is that each PS4 would have to come with a cell processor installed to make the games work. (And it'd have to have special firmware made so that the system could take advantage of the greater RAM amount/speed and GPU of the PS4 without breaking things.) But that would increase cost significantly. So they'd either have to:
1- charge more for each PS4. And that would run the risk of Microsoft undercutting them in price even more so.
2- take a profit hit on each PS4. They did that to sell PS3s... it's unlikely they'd want to repeat that again with the PS4 (especially after it's been selling so well).
Therefore, having the PS Now to provide backwards compatibility via streaming is somewhat of an option, even if it isn't exactly perfect.
It would be nice though if they made it so that you could play games via streaming that you already owned for free by inserting the disc. (So you put a copy of a game in and it'd recognise it as a PS3 game then ask you to stream it via PS Now.) But it's unlikely they'd do that simply because of the cost of streaming that much data.
Now, all that stated, I would pay more for a more expensive PS4 that had backwards compatibility. But whether or not Sony wants to make that an option is unknown. Given how quick the PS4 has been adopted and how well it's selling... I really can't see them being all that interested in offering it though. Especially not when PS Now exists and they're remaking select games from last gen on PS4 (for those that may have missed them).