Although I have a 4 wheeler I do understand your concern. I have had lots of classic cars and bikes over the years and there is no denying that a Morgan in whatever form will possibly require more of your attention than a 'normal' car, but no more than any other classic type car or bike.
But doing so is really part of the enjoyment for many if not all.. I would suggest there is a small community of owners that just jump in and go without much thought to maintenance and care and their cars do suffer as a result. Most fiddle and faff about to keep them bright and rust free, if you are the sort that likes doing that then I'd go for it.. if you are not, best avoid one.
