You're using the words 'Irish Heritage' there a bit loosely. Dal Riatta barely covered even the slightest part of Northern Ireland.

I wouldn't say that the English know much about the Anglo-Saxons. You'd probably find that most people have heard of Alfred the Great, and the Harold who lost at Hastings. I don't think that most would remember anything about the Heptarchy and the Danelaw; nor would they remember the Battle of Stamford Bridge or that Harold's surname was Godwinson. Those are probably the most memorable characters (in the 1066 and All That sense).

The importance of Dalriada seems to be debated, to the extent that it's not even agreed what happened to the Picts (or to what extent they existed). Whatever happened, the consequences were largely over-written politically and linguistically by the Davidian Reforms. The links with Ireland were based on Gaelic culture, but Lowland Scots came to dominate most of Scotland. Gaelic and the associated culture was often looked down on as "Erse". Similarly the religious links were probably eroded by the Viking attacks on Iona, and were severed almost entirely by the rise of Presbyterianism in Scotland - the major exception being that the only Gaelic translation of the Bible until the mid-19C was in Irish Gaelic, hence this one was used in churches in the regions of Scotland using Scots Gaelic.

A further factor is the plantation of Ulster with Presbyterian Scots in the early 1600s - these people still identify themselves as Ulster Scots and maintain a separation from the native Irish to this day (hence the Troubles). This tends to discourage identification of Scottish culture with Irish antecedants.

So in summary - such links as there were happened in a poorly documented period of history, and various political and religious events have eroded any identification with Ireland over the centuries since then.

I would recommend Hobsbaum's "The invention of tradition". It has been a while since I have read it but I know he discusses at least some aspects of it at some point.

edit: I do remember him trying to make a point about the kilt and bagpipe being propegated somehow by Sir Walter Scott for some interesting political reason. The book itself should be read with a grain of salt IMO because while it is a really cool idea it (again IMO) seems to pretend that cultures never did this previously and in fact why wouldn't they have? He may bring it up himself but within many colonial conquests these things have happened.

Kenneth MacAlpin didn't really found Scotland, he was just an opportunistic Pictish king. He's cited as the first king, but you would be closed to the truth in saying his grandson Constantine II founded what would be Scotland when he merged the Gaels and Picts to form the Kingdom of Alba.