I can see a plausible reason: it might shave off several hundreds of bytes of transmitting data when one views the beatmap page. If there are like 100k views per day, peppy shaved off several tens of megabytes of data, reducing bandwidth.
If that (bandwidth conservation) isn't the reason though, I prefer colored short name over long name or short name. For me, it's easier to see. Heck; just use the standard mod pictures.
Or otherwise, adapted from some website: Always display all mods, in the same order. However, nonused mods can be grayed out. Something like this:
EZ NF HF HR SD DT HD FL SO nK
For variation mods (PF, NC, FI, the key mods), just replace the corresponding text:
EZ NF HF HR PF NC FI FL SO 8K
The used mods can also be colored (obviously use dark colors, otherwise they aren't seen). To conserve space (horizontal space is important, some website says), some mods that negate each other (EZ-HR, NF-SD, HF-DT) can be put in the same spot:
HR SD HF HD FL SO nK
Well. I just hope the above idea doesn't stray from the topic.