On the other hand, the Intrepid was already a jinxed name in Starfleet service. Perhaps jinxes don't count for much in that organization?
One wonders which "old" Intrepid the "Force of Nature" ship might have been if it weren't the class leader for the VOY hero ship type. The ages-old Excelsior class vessel that rescued Worf in 2346 and wasn't heard of since? A successor from, say, the Ambassador or Nebula class? A sister ship to E-D? Even Memory Beta offers no such in-between vessels, despite there being no fanfic or novel continuation for the adventures of the old Excelsior beyond 2346 and thus no contradiction for the introduction of in-betweeners in fanfic or novels.
In the novel Crossover, set between TNG S7 and Generations, there was a Galaxy class Intrepid that was commanded by the son/grandson of Riley from TOS.