I have a feeling that perhaps the real reason why DMC’s Dante was redesigned as the game got rebooted in the early 2010s might have to do with Dante’s Inferno. Both of them garnered controversy and for the former, it’s got to do with distancing itself from Dante’s Inferno.
Possibly to be not trapped in its shadow at the time even when the DMC reboot had the opportunity to base its Dante more closely after the poet that inspired him. The DMC reboot would’ve been a more respectful version of Dante’s Inferno.
By basing Dante after his real life counterpart, the reboot would’ve been more successful in the west and the latter’s work is part of the western canon. It too would be criticised but would’ve fared better in hindsight.