I’ll start with the necessary disclaimer that it’s not my card, people can do whatever they want with their cards. I’m not going to stand in the way or say someone is doing something wrong. That being said I do have an opinion on the topic.
My grand theory of this hobby is that people primarily seek to “grail-ify” everything. We generally collect cards that are mass-produced so in order to justify the value of items, we come up with ways explain why our items are better than all other other near-identical items out there.
If you look around it’s evident everywhere. The “better than gem mint” grades are valuable because of grailification, not because of any meaningful difference in condition. Errors and miscuts are valued because of grailification - it’s why people care about a red dot on a Blastoise or why a beginner person will by default assume any error equates to value. It’s why swirls, which started off as a novelty/joke, became a serious thing.
This grailification is especially noticeable in the autograph collectors. All autos are 1-of-1 so it’s never enough to just have an autograph, you need to grailify it somehow. You need the rarest, most valuable card the artist has done. You need the jumbo/energy/blank card so it’s a bigger sketch than everyone else. You need to be intentionally different than everyone else to the point of absurdity. Basically if you want an example of what I am talking about, just look here Pokemon Cringe - #5 by pfm
I think a signed trophy card is just another example of the most common impulse in this hobby just with another zero on the dollar value. It’s the “how can I make this item more of a grail”. I think for a lot of people, they see a signature as additive or multiplicative of value regardless of the card. I don’t personally agree with this.
To inject some nuance, I don’t think grailification is only a bad thing. I think there are healthy ways to engage with the idea. Buying a card in a better condition makes sense, if the difference in condition is meaningful to you. Error cards and autographs are actually cool. I think really the important thing is in understanding where the value is derived from - internally or externally. If you do something because you find it cool, that’s fantastic. If you do something because you are seeking the external validation of your peers in the hobby… it isn’t necessarily a bad thing but I really think it’s deserving of some self-reflection. “Would I care about this thing if I couldn’t share it online?” - a good question to be asking.
And I guess ultimately my opinion on a signed trophy is based on all this. If it’s intrinsically motivated, I’m very happy for the person. If it’s extrinsically motivated, I guess it’s fair game to judge it however you want to.