I think Scott's being aged up in the tv series makes his story that more poignant and interesting. From a hockey perspective it changes his story entirely and I'll explain to you why.
In the books Scott is only 3 years older than Ilya and Shane are. So when Ilya makes those jokes about Scott being old, washed and a dinosaur etc. it's all relatively in good fun because the age difference isn't that big.
However in the show François Arnaud the actor who plays Scott is 40, and so i'd say this Scott would be in his mid to late 30s, maybe even 40. From a hockey perspective that changes his story entirely.
Hockey is a young man's game. Most players retire when they are in their mid to late 30s and then they have had a long career. Plenty of players retire much earlier.
Winning a Stanley Cup is even more of a young mans game. The average age of Stanley Cup winning core is 28 but a lot of these players are quite a bit younger (average age of a Cup winning Captain is 29).
Secondly (and we don't know this for sure because it isn't mentioned anywhere in the books) but we can asume with Scott being such an established player in both the books and the series that he was a high draft pick, maybe even a number 1 draft pick. Why does this matter you may ask? Well, because this brings even more pressure to win.
If you're the star player of your team and a number one draft pick you're expected to win a Cup. The current 1st over-all pick who has gone the longest without winning a Stanley Cup was Taylor Hall of the Carolina Hurricanes (he won the Cup this sunday after playing 16 seasons, at 34)
So imagine if you will you're Scott Hunter and you're in your mid to late 30s and you're in the last stages of your career and you've never won a Cup? Combine that with the fact that you're not only a first overal draft pick, but also the captain and star player of a franchise that hasn't won a cup since 1994. The pressure to win one would be relentless. Constant questions in the media about how you're biological clock is ticking and time is running out etc.
And Scott winning at that age is fucking impresive. Winning a Cup is hard, it's brutal both mentally and physically. And that's for players in their prime, Scott in his late 30s would be well passed his. (This means that Ilya's chirps would hit a lot closer to home for Scott in the show as compared to the books)
I'm not saying it doesn't happen. Captain Jordan Staal won the Cup on sunday with the Canes and he was 37 (but he made history with being the oldest player ever to win the Conn Smythe trophy). Brad Marchand won two back to back Cups with Florida in '24 and '25 (not as s captain) when he was 37.
But the crucial differende between these two men and Scott, is that both of them already won a cup Staal with the Penguins in '09 and Marchand in 2011 with the Bruins) They already proved themselves capable of winning a Cup. Scott at that age has not.
So when he finnally does win the Stanley Cup it hits that much harder and makes it that more impressive and special. It also makes his story so much more heartbreaking because he hid who was from the world for so much longer.