I might be in a minority here, but I think records are just as prestigious as trophies. Ideally, you want both, but the very definition of a record is "the best performance or most remarkable event of its kind that has been officially measured and noted". I see the words 'best' and 'remarkable', the same words that would be used to describe a champion.
Like trophies, some records are worth more than others, but there can't be any argument about the worth of this one. Every teams primary aim is to win every match (by extension, not losing), so if we do get it, it is very valid to say, no other team has been able to achieve this while giving it their best. It's something to be proud of.
There is also usually a new champion every year. Loads of teams have been champions. However, there is usually only one, or at most a handful of record holders. Case in point is Arsenal who have been mostly irrelevant recently, but their undefeated record is still remembered. An even greater case is Preston North End, I can't remember Sunderland, Everton, etc's trophies mentioned as much as that one season from PNE, despite probably no one here being alive for it.
Finally, and I'm not trying to insult anyone, but this feeling among some fans, that some things are small time and beneath them is cringeworthy. Newsflash, unless you actively contribute to the club as a player, or staff in some capacity, you have nothing to be so smug about. The fans of the "small teams" that you belittle could just as easily choose to support Manchester united or any other big club.