It is... if by "Successful" you mean "money maker"!
PS4 isn't just Sony's Most Successful Console to Date, it's the most Successful Console ever!

Yeah, but in May-June 2014, the PS3 was selling 45-50k per week on VGChartz.  Right now the PS4 is down at 31k.  Keep in mind that the PS3 was considered as being a failure for Sony.  Unless Sony is going to announce another price-cut for the PS4, I don't see this trajectory changing much.  Honestly, if the PS4 was going to get another price-cut, then it should have had it already.

1) As far as I know, Sony has never released the actual profits of the PS2, and I've spent a fair amount of time looking at their annual reports for that time period.  If you have a link to where Sony themselves has released those numbers, then I would be interested in seeing that.  Instead that looks like the total profit of Sony's game division between the PS1 and PS3 release dates.  However the PS2 is known for having great legs and kept selling fairly well even after the PS3 released.  The PS2's total profits have been masked by the PS3's losses, and in Sony's reports all profits/losses from that time period were lumped together and not broken down by system.

2) Your numbers are not adjusted for inflation.

I still think the PS4 is more profitable than the PS2, but this isn't as one sided as you are making it out.

The link i sent you mentions it, and they don't mention anything about the PS3's $5.5b loss. 

"According to Critical Hit, PlayStation generated more profit in the fiscal year of 2018 than it did over the course of the entire PS2 era, which by console sales, was its most successful era ever. The total amount of profit made by the PS2 was $2.22 billion"

Not entirely sure how accurate their figures are however it would be sourced from somewhere.

If you compare it against other Sony consoles? Hell yeah.

The PS4 might not overtake the PS2 overall numbers in the end, but Sony profited a billion times more due to games generally selling better on it but most importantly, because it was during that gen that its first party sales simply exploded. Many of its internal titles did absurd numbers, and brought Sony alot of fame(as a game developer, not just as a hardware developer) and alot of beloved franchises.

If you compare against other consoles? No. It porbably won't reach the insane profits that the DS gave Nintendo, and the Switch will beat the PS4 in most regards in this topic.Hardware sales, first party software sales. The only two that it will probably lose is subscription numbers for their services and third party sales, but its probably not enough to offset the other points.

Having said that, the PS4 is a economical success story in every way you slice it. Sony deserves all the praise, given that the PS4 is a great console, and I really hope that Sony keeps the train going with the PS5. Ratchet and Clank Rift Apart is looking stupidly good.

Basically, the success of PS4 is standing over the shoulders of PS2.

At this point who decides how much a console sells and stop being supported is the customers not platform maker.

Sony sure could cut the price, but the added sales with a lower price wouldn't bring additional profit, some time ago I've done a good analysis on cutting 100USD to sell 10M more consoles and the numbers didn't match.

PS2 AND PS4 are perfect for Gamer. The most Games, the best high quality-Games and the biggest Exclusives. Love both console's very much.
And the future is: PlayStation 5!

Ok, that reads like an ad.

Is it an Ad? Idk.

Sure, PS2 sold more hardware, but PS2 also had less/weaker competition at the time as well.
PS4 sold software like it was free, while competing against what was, or should have been, much stronger competition.

I'd say their success is pretty much equal for one main reason. While it was likely both would be a success in general, nobody anticipated how swiftly either of them would absolutely crush it, prior to their initial unveilings and specs being officially presented.