What about, and I say this as a long-term martial arts practitioner, the man who has practiced 3 kicks 3300 times each (with one rep to spare)?
And I am not saying it provocatively, the one-10000, 10000-one is a straw-man of course, but how many techniques to add to your competition arsenal is not an easy question to answer.
As far as I remember, Ono, one of the most successful judokas of the modern era, has maybe uchi-mata, seoi, osoto, tomoe-nage.
Teddy Riner, who had dominated the heavy-weight category for more than 10 years, basically had only uchi-mata, plus refusing to engage, running out of bounds. I remember a clock-choke and a few pins too.
On the other hand, in wrestling you had someone like Cael Sanderson, who won the gold medal in 2004 and had one technique, the ankle pick. Saitiev, who won 3 gold medals in different Olympics, had instead a big variety of technique.
Let's take judo. While nobody has, say, 15 competition ready techniques, a critical decision needs to be made between 3 or 5, say. So it is not as easy as saying: specialize! In addition to find the right (for you, considering your opponents) techniques to specialize in.