They were ordered to make ENT while VOY was still on, that's why Ken Biller took over VOY in the last season. Still under contract.
And they didn't have the degree of control that JMS had over all his work (because he was the actual creator of the B5 universe) so his strategy wouldn't work for them.
As for the "DS9 was good because VOY sucked" thing, that's another lie. DS9 had its freedom due to being syndicated, not because VOY took all the attention. Berman was as involved with DS9 as he was with VOY.
Actually, the strategy holds. JMS has always maintained that he won't return to the Crusade storyline as that effectively belongs to TNT/WBs. Given that JMS has used one of the characters back in the B5 main universe after the cancellation it would suggest that JMS has control over the characters to some degree at least. Hence, it's unlikely that TNT would have been able to continue with the show under different direction.
That however, wasn't the point. UPN would undoubtedly have continued knocking out Star Trek whether it was Berman/Braga or someone else. There were definitely ways for them to check out, especially from Enterprise. Yet they chose to stay. What would the point be of them leaving? Presumably their reputations would have benefitted. Whether it's true or not, the perception is that they delivered Star Trek's death knell with Enterprise. They'd also have been freed up for other projects. If Berman and Braga are that great, why would they need the Star Trek crutch to keep them going? The Straczynski situation was highlighted to show that there are ways of maneuvering away from a show without falling foul of the legalities contained within contracts.