Agreed the 146 seems overkill - believe Scot Airways looked at doing Carlisle to London City a while ago with one of their Do 328s, a 30 seat turboprop, and decided against it.
There is considerable industry at Workington/Whitehaven whose nearest airports are Manchester or Newcastle which take hours to get to (please don't get clever and say their nearest airport is Ronaldsway !), and there's Dumfries and area in Scotland, likewise a long way from Prestwick. Both would also find Carlisle convenient. LCY could have given "proper" connections to Paris, Brussels, Amsterdam, Frankfurt etc.
Yer showing yer age now dada !
Shall I really show my age and recall Autair doing Luton-Blackpool-Carlisle-Dundee with 748s in the 1960s !