There are a number of issues here some are being glossed over in discussion of fairly minor issues.
Of course a router can be used in the construction of a door however:
Hinge and lock fitting , will need jigs as described :expensive (bought) time (homemade)
Shaping with a bearing guided ogee bit and large (preferably transparent) base plate will very quickly shape the panel openings on the almost completed door. The mitred strips to retain the paneling material can be made withe the same kit .
Withe use of specialist bit sets (and router table) you can do much of the carcase jointing of the door. More unavoidable expense here.
Now what other machinery might you need? When I made a ten light internal door a few years ago I used an Elu band saw for all cutting to length and mitring A table saw would be a less safe alternative – I like a full set of fingers! and a biscuit jointer.
All the timber was standard PAR and was about 10% of a big lot bought for a job that was much less critical, wider strips were made gluing side by side and only needed minimal sanding.
Making ONE door may be a lot of trouble and expense but I found rewarding having no large tool purchases.
Finally doors are big and even in pine quite heavy so you will need a biggish working space (two trestles outside when nearing completion was ideal) and possible lifting assistance.
Making a proper door from scratch is surely on any woodworkers bucketlist
Happy Chippering
John