Advantages of making Tokyo your final stop: If you expect to do a lot of shopping, Tokyo (and perhaps its suburbs) would be the best place in Japan to load up on purchases. It would be inconvenient to have to carry all your purchases to Takayama, Kyoto, Osaka, and then back to Tokyo. Also, if you take advantage of tax-free shopping, you are required to carry all your purchases home on the plane; you may not mail those purchases home and still take advantage of the tax-free system.
Disadvantages of making Tokyo your final stop: You will have to be awake and alert after your flight to get to the right trains and make transfers on the way to Takayama. (I was once so tired after my flight to Japan that I got on a train going in the wrong direction.) There is also plenty of good shopping in Osaka and Kyoto.
It might be easier to take the train to Kyoto or Osaka (rather than Takayama) right after the flight. Or just fly to Osaka or Nagoya and return home from Tokyo.
Most first-time tourists start their trips in Tokyo, and most package tours do the same thing. Maybe it's because it's cheaper to fly to Tokyo than other Japanese airports, and most people don't want to do a long train ride after a long flight. Maybe it's a holdover from the old days, when there were significantly more English-speaking people in Tokyo compared to other parts of Japan and it was easier to adjust by starting in Tokyo. That difference has narrowed to the point where it's a minor issue.
My advice: Consider flying to Osaka (close to Kyoto and Osaka) or Nagoya (Centrair, the closest major airport to Takayama), start your trip in a city that's close to your arrival airport, and return home from Tokyo. If it's not feasible to use Osaka or Nagoya airports, fly to Tokyo and immediately take the train to Kyoto (fewer connections than going to Takayama). Limit your shopping until you get to Tokyo. However, if you find something you like at Muji or Uniqlo anywhere in Japan, make an exception and grab it; you may not find it again later in your trip.
I typically fly home from Fukuoka Airport, the closest airport to the Kyushu ceramics district, so I don't have to schlep my ceramics purchases all around the country.