Is there such a thing as a complete martial art?

Kano's early Judo included distinctive striking techniques (atemi waza), and training in many weapons, as well as throws, groundwork, and revival techniques, all distilled from multiple jiu-jitsu ryu.  When Funakoshi brought Karate to Japan from Okinawa there was cross-fertilization with Judo, similarly with Ueshiba's aikido (Tomiki, I believe, was ranked 9th dan in both arts).

So judo was an evolving composite, from which specialist streams have emerged.  You can see echoes of some of this stuff in the higher judo katas, but overall there seems to have been a loss of heritage, at least in mainstream Olympic Judo, due to multiple factors, including: optimization for a particular rule-set, with victory in competition as the main goal; popularization as a national physical exercise regime suitable for dissemination through high schools; and the banning of most martial arts practice in Japan following its defeat in WWII.

Similarly, chinese boxing (kung fu) styles have evolved, combined and recombined over the centuries.

There are broader and narrower martial arts.  Training in a broader martial art as a base has much to recommend it, if you're in it for the long term.