Yes it is feasible, in fact it is no problem at all for an aircraft to perform a Continuous Descent Approach (CDA). The difficulty is that Air Traffic Control (ATC) can not predict accurately how the progress of the aircraft will be during the CDA, so they will need to add extra spacing from other aircraft to ensure safe separation. This reduces the capacity of the airport. Therefore CDA's are only used when there is no need for high runway throughput.
For example, Amsterdam airport uses CDA's from Top of Descent during the night hours and in the early morning. Around 6.30 AM local time they can no longer offer CDA's without risking separation conflicts with other aircraft as traffic start to increase rapidly around that time. They will need to vector and put aircraft on doglegs to ensure separation minima are honoured.