A non-backwards compatible PlayStation 5 would be suicidal
Why shouldn't it be BC?
Suicidal? No it wouldn't. Not even close. Look at PS4. When you have the first party studios, exclusives and IP's that Sony has, it doesn't need BC whatsoever. Add in remasters, definitive editions, etc. and it definitely doesn't need it. Factor in the $380M that Sony spent on Gaikai and I just don't see it happening.
As for why it shouldn't be, that's simple...why should it? Consoles have done great and survived without it and why do people even want it? When I buy a new gen console, the LAST thing I want is to play past gen games, remasters or those definitive editions simply because whatever I wanted to play, I did and those I missed, oh well. Time to move on.
I know a lot of people praise Microsoft for BC but let's be realistic, the exclusives on Xbox 360 and overall lineup crushes Xbox One. When you get the biggest cheer and ovation for an original 15 year old Xbox game in your press conference, that should probably tell them something which is their current software is lacking.
I don't see this happening with Sony due to their studios, IP's, etc. For me personally, BC does nothing for me. It's not going to make me buy your console. Also, if BC is added in at the expense of say, a better CPU or more RAM, I easily say no to BC. Granted, that's probably not how it works but in case you don't get my point, it's that with every new generation and console, I want games to advance and get better, not worry about what was already done a decade earlier.
I think that while BC is a fan favorite PR move, it literally does almost nothing to boost your sales long term. Xbox One had a little bump but that's it. If it was so important, Xbox One would be sitting at 60m+, not 35m. I just think that it's overrated and I don't want to see any money, time, resources spent on it when I care more about the future games as opposed to the past.
Of course, this is just my own personal opinion in regards to me and what I care about in gaming. BC simply isn't one of them, never has been and never will be.
For Sony, with Gaikai, I simply don't see them doing it and to be honest, there's really no reason or incentive to do it.
For gamers, I get that some may want to carry over their previous gen games over to their next console but most publishers don't want this simply because they know that they can sell you the same game more than once and you'll most likely buy it again. I also think that gamers make it far bigger than what it actually is.
Also, up until PS2, there was never any BC. Nintendo/Sega never had it and no one complained. All of a sudden, gamers want to complain about it? Of course, in fairness, gamers complain about anything and everything nowadays but still, it's not needed.
An easier solution is just keep your old hardware. Problem solved. For me, once I move on to the next generation of consoles, I never ever go back. Granted, there's plenty of games since NES that I wanted to play at one time or another but didn't for whatever reason. I'm not going to go back playing all these old obsolete games when I can be playing current games.
Again, this is just my own personal opinion on BC as I simply think that it's overrated and doesn't make as big of an impact as some may think. Business wise, I just don't see why Sony would do BC when they have Gaikai.