Xavi is catalan (shorter form of the name Xavier) and in Catalan "x" has exactly the "sh" sound. To get the "ch" sound you need to use "tx". And yes, most people - even natives - pronounce Xavi badly, due to Castillan influence on Catalan, and the lack of the "sh" sound in Castillan.
Yes Catalans haver no problem with the "x" :) but it's just with the name that is mispronounced due to the Castillan overlap. I think that "caixa" with the "i" before the "x" makes it easier also for Castillans (although it's funny to hear them pronounce it). There is also the fact that both speakers have serious issues with words starting with "s" + consonant, so my theory is that "shavi" is also affected, while "chavi" is far easier.
> most people - even natives - pronounce Xavi badly, due to...the lack of the "sh" sound in Castillan
Catalans seem to pronounce "caixa" fine, so I think they _could_ say "Shabi"... But this does back up your larger point about "x" -> "sh" in Catalan.