I always thought at Arrows in 1996 Rosset was in the "pay driver" role (replacing Inoue) and Verstappen was in the "talented one" role (replacing Morbidelli). Any money Jos brought would have been a bonus, and probably why they took him over Morbidelli but I don't think someone of his record and, at the time, potential, was exactly unworthy of a seat at the 8th best team in F1 at the time.
Come 2000/01, Arrows seemed to have the strategy of hiring two decent drivers who could also bring some sponsorship, aside from Verstappen, de la Rosa brought Repsol, and then Bernoldi brought Red Bull at a time when RBR and Toro Rosso/Alpha Tauri didn't exist, but I wouldn't consider any of them full-blown pay drivers, which I guess I define in my own head as drivers who wouldn't have a remote shot of an F1 seat without bringing lots of money.
On a trip down archive-street, I've not been able to find an actual Arrows announcement of the drivers for 1996(!), just a couple of "even though Arrows hasn't confirmed; this is how it will be" articles, which have turned out to be correct. Anyway.
Arrows 1996 sponsors:
"The team is to receive backing from the soft drinks firm Hype, although most of the sponsorship money will have come from the drivers. The team has failed to secure backing from a motor manufacturer for the Hart V8, and so the engines will once again be known only as Harts."
Morbidelli (and Inoue):
"1995 Arrows driver Gianni Morbidelli does not have the money to secure an F1 drive this year, while Taki Inoue is now trying to take his pot of Japanese gold to Minardi."
From that is seems like money weren't just a bonus for 1996-Arrows, but something that was needed to get the seat.
TWR Arrows was horribly managed. 2000 seemed to be a case of going to two talents (even if they did bring some money) but then in 2001 de la Rosa was replaced by a Bernoldi and his Red Bull backing.
But I tend to define a pay driver like you do. Someone who wouldn’t be in a race seat without brining a lot of money. Where is gets difficult is determining if the money comes from being talented enough to earn a potential sponsorship or just from a business connection.
Arrows wouldn't survived until 2003 anyway, but they might've survived until the end of 2002 at least if they'd kept Verstappen (as the contract said) and not gotten rid of him, and his sponsors, and having to pay Verstappen for it, and then replacing him with Frentzen, even though Frentzen probably was the better driver of the two.
Pay driver definitions are a fun thing. Our definition are the same, but for me it doesn't really matter how talented a guy is, for me it's more a case of "had he been able to race if not for the money". If the answer is "no" then he is a pay driver, at least for that season.
Didn't know Jos came from such a poor background. No matter how he got into F1 he does not belong on a list of worst pay drivers. Max is a better driver than Jos was, which Jos has admitted, but he was a very competent grand prix driver in his own right. Imo both Ericsson and Latifi who I've seen mentioned here are competent drivers. Not superstars obviously, but not as bad as they are sometimes made out to be.
I've been following F1 since 2000 and looking through the grids since then my candidates would be:
Yuji Ide
Oh, I don't mean that Verstappen should be mentioned in any discussion of anything "worst" in F1 (maybe one of the worst managed careers?). It was just a good example on a driver that might be counted as a pay driver (or not) depending on who you ask.
Did Ide actually bring any money? In fact, did any Super Aguri driver bring money? I can't even find anything that states that Yamamoto brought sponsors for his Aguri-drive. In hindsight I guess Aguri should've worked harder to get Kosuke Matsuura in the team, at least he had some experience and results in Europe.