On a quick check of some the greatest batsmen for other countries.
For Australia Bradman, Border, Waugh, Harvey and McCabe all average more away, while Greg Chappell is about even. As would be expected given Australian pitches of the 21st Century, the modern greats - Smith, Ponting, Hayden, Clarke - are heavily home skewed. Smith, to be fair, is 64/54 so is awesome either way. Clarke the worst HTB with a 62/39 split.
For England Barrington, Hammond and Hobbs all average much higher away, while we know May and Compton are HTBs. Hutton is about even while Sutcliffe skews home but like Smith is great either way with a 64/56 split. I was a bit surprised by Root averaging more at home than away, given how difficult we perceive batting in England to be.