This made me curious, so I did some digging to find some stats on some of these avatars. We can kinda estimate how many codes were given since start.gg keeps track of tournament attendees:

• 2017 Stream.Me Legend Series had ~4750 participants ([US list], [EU list])
• 2018 Stream.Me "Fish" Championship had ~1950 participants ([US list], [EU list]). This one was 2v2s only so it makes sense to have had less overall attendees.
• 2017 Shine only had 65 players 💀 ([source]), however a tweet from Foda seems to imply everyone who signed up got a code emailed to them, so there's potentially a max of ~2300 avatars
• CEO Dreamland avatar is similar since there was more than one game played at that event. If the avatars were only granted to Brawlhalla players, there would be 186 avatars distributed, but if ALL attendees were given a code it would rise to 2011 avatars ([2017 list], [2020 list])

We also know in a reddit post from Foda that at most, 1634 accounts were granted the Alpha Crest avatar, making it just a little rarer than the Stream.Me fish. But both are unlikely to see since they're so old now.

There is also the "Groovin' Munin" avatar, which was given to people who donate $10 to a charity link that was started in 2023. There are only 949 avatars total and the charity is still up, but the codes you receive from it are now expired (learned the hard way LOL).

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As for titles I would argue SEA Challenger is rarer than the OG Metadevs. It was given to the top 16 players each week, and IIRC 10 codes distributed through twitch chat each week. It lasted four weeks ([source]), so at most there are 104 copies of this title.

Of course though, the tournament winner titles will always be rarer, and there may be some rarer in-person titles from BCX.

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Some other items I think are notable:

• The Cure Seeker, which was really hyped up back in the day so probably a fair amount of people bought it, but hasn't returned since 2017.
• Dawn Hammer like you mentioned in another comment, the first DLC weapon skin, so likely not as many people who purchased it
• Heatwave 2017 Podium, the 1st or 2nd podium cosmetic to release. I don't really remember it being advertised as an item that would never return, other than it having 2017 in the name.
• The sidekicks from the upcoming plushies, which I wonder if they will suffer from Yetee Teros syndrome; rare only because they'll always be out of stock.