I did chase this signed theme for a long time, but I was not sending them myself, just buying when they showed up on eBay or on trade boards. The only 3 I ever personally sent were Rose and Dick Allen after never finding any to buy and seeing decently priced TTM opportunities and Scott Radinsky of all people, because nobody seemed to have one.
I was nearly 100% complete from 1960-2000 with a decent start on the 2010s and it just fell apart. The set had become overly frustrating though, because each new year it was always loaded with super hyped players, many of whom never amount to much beyond their rookie season. Then it seemed, a fair chunk of the very best and brightest were on the team, making it impossible to afford most right out of the gate (Trout, Bryant, etc), if you could even find one available to buy. Another factor that has lead to my demise is that people just don't seem to be sending base Topps cards as much as others like Heritage, AG, etc.
If you look back at the rosters, in the early years there was a disproportionate amount of so-so players and only a handful of stars/HOFers, which made filling in the gaps fairly easy. A lot of older players are now deceased and then there is the ultimate whale of this set, Thurman Munson. Both a near impossible find and if you did find one, better be rich if you want to buy it! Also never could land Ichiro or Jeter, which partially lead to my decision to stop trying so hard. I still will buy them if I see them, but my dream of completion has been shattered forever!
Some really great cards if anyone wanted to make a run. At the time I quit actively seeking them, my most wanted commons were:
1995 Ryan Klesko - I swear there must be some story behind this card, maybe he just won't sign it??? It seems like every other card ever made of his can be found signed for a buck, but I can't find this one card to save my life!
2002 Tsuyoshi Shinjo - Several Japanese players made the team in the 90s/00s, including Ichiro. My fear was a player like that returning to their home country, like some older Central & South American players, never to be heard from again. his career was short and he either didn't sign much of people either weren't selling or getting them to begin with. I believe he did return to Japan. Have never seen one, but have a couple other signed cards.