i think Sony will do all the BC on PS5 so that it will be more appealing than rather just a more powerful next gen PlayStation

The PS4 doesn't need backwards compatibility. PlayStation actually has appealing exclusives, and a good quantity at that. Microsoft rolled out their compatibility feature to backfill their lack of exclusives, if backwards compatibility was a such a great benefit - then Xbox One would have covered some lost ground with it. But they haven't and PS4 still outsells the X1 two to one, with the Switch coming right up on their meager 35 Million unit average from being on the market for 5 years.

The PS1 and PS2 had a lot of exclusives too, that didn't stop their successors from being backwards compatible.

Actually if you take a look at what they have done in the past three years, they really have been consumer friendly (besides the scalebound cancellation, even though I feel like Platinum deserves a lot of the blame, but I digress).

That would be great if it did because I still need to finish Red Dead Redemption, and several other PS3 games. And I don't really have a lot of incentive to plug in my PS3 when I've got the PS4 and a bunch of games on there.

As a consumer.. They should. Plus having ps2 and ps4 to play the whole library saves a lot of space... butttttt in a business stand point they shouldn't since a lot of people double dip :p

How much does backwards compatibility matter?  Well lets look at the performance of Nintendo, Sony and Microsoft consoles.  Some of them had BC and some didn't.  Below I've ranked each console based on hardware sales and market share on a 1-10 scale.  Obviously I left off consoles that were firsts in their line (NES, PS1, etc...) and I left off Switch because it's so recent.  Here are the results:

There certainly is a strong correlation between BC and market success.  It doesn't guarantee market success, but it sure doesn't hurt either.

Actually, now that you mention it, a lot of successful consoles had backwards compatibility. The PS2, PS3, Wii, GBA, DS, 3DS, 360, MD, etc.

I know right?

If nothing else, consumers really favor consoles that are consumer friendly, and BC is one really nice, consumer friendly feature.  The PS4 got away with not having it, because both the XB1 and Wii U seemed even less consumer friendly at launch than the PS4 did.

I think I recall it was due to the architecture of the PS3 that made it difficult to have the PS4 be BC with PS3. Apparently, in order to do it, they'd have to put in the PS3 core processor as well to do it, which didn't seem worth it. And I'm not sure if having it be BC with PS2 and 1 would make much sense, since mostly people who owned PS2 and 1 games would be able to make use of that feature, and not people new to Playstation.