I get your point that if Splitter is seen as a fit, then how much moreso ought DH be.
That helps.
But given deeper thought, what makes Splitter valuable--again, specifically on offense--is his familiarity with the system and the passing ability that you mention... and, importantly, that he can actually shoot from as far as 15 feet... all of which are superior to DH.
And building on that thought... I wouldn't say that Bud "only values stretch bigs," if by stretch bigs we're speaking of 3 point shooting. I would say Bud values bigs who can shoot. Because, clearly, what allowed Teague or Schröder to make those drives to the rim was the threat of Horf standing out there near the free throw line, where he's deadly.
Can't do that with DH.