I don't see how EA creating their biggest rival is anything but a bad decision for them. Had they licenses they would have a monopoly and probably millions of more sales.

yeah but was the point of this decision that they want to fuck with SEGA, or was the point of this decision that they didn't want to invest development resources into something that they (correctly, unfortunately) expected was going to be a dead end? It would've been the right decision with what they knew at the time but looking back in hindsight they would've been far better off if they had just made a couple shovelware games for the Dreamcast if that's all it would've taken to prevent 2k sports from ever existing.

Also the last football game in the series, ESPN NFL 2k5 (actually released in 2004 a few months before they sold the studio to Take-Two) was seen as the primary reason why EA payed off the NFL to stop selling licenses to their competitors; so it's indisputable that the 2k-sports brand had a negative impact on EA's bottom line while it was still a SEGA subsidiary.