Unless Varley lost the 1305-E to not honorable reasons. Kirk took risks with the Enterprise all the time, but they still gave him another ship (after he saved Earth.) Varley could've lost the 1305-E on a mission but the new ship that they gave to him kept the original registry when she was re-named to Yamato as a reminder that it didn't deserve a letter registry. Varley could've been going on extra risky, rogue missions just to rebuild his credibility back
It wouldn't be too hard to look at the 3 month gap between ST3 and ST4 to ask the same question of Kirk getting another ship
that almost got destroyed again in ST5. Or in the case of Sisko's Defiant, they were awarded a new ship and were allowed to KEEP the original registry - totally screwing the whole "letter" concept.