Interlining across tickets also takes time and that slows down check-in lines. There are all manner of reasons why carriers have and continue to end this service.
It can be particularly problematic for people who must clear immigration at a transfer point in order to reclaim a bag and check in and may be required to obtain a visa or may indeed not be admissible.
Fortunately, if OP is a UK, ROI, or US national, this particular circumstance will not cause an immigration issue.