I read that someone asked if this was the case why hadn't Shakespeare written about it?

This cook book appeared in 1615 and Shakespeare died in 1616 so he may not have heard of it in time. Had he done so he may well have beaten Rabbie to it and popularised a dish which cannot really be said to have taken off in England, whatever its origin.

Forsooth! This pudding of our sceptr'd Isle!
This seat of Kings! Yet who dare'st deny the smile
On English lips, when thereupon they taste
And knowing that t'was o'er the Scots outpaced!
Let them prattle! Let them waste their breath!
But there is no Haggis in Macbeth!