Not necessarily! Ski socks with no arch support have a uniform construction through the midfoot, meaning there's no built-in elastic or compression band squeezing your arch. This simpler design is actually preferred by some skiers, especially racers who want the most minimal, unobtrusive sock possible between their foot and boot.
The main trade-off is that without arch compression, the sock may shift slightly on your foot during the day. For most skiers, that's a downside — but if you have a boot that fits like a glove and you don't want any extra pressure points, the clean construction can feel great.
No arch support is also a good choice if you're sensitive to compression around your midfoot or if you already use custom footbeds that provide the arch support you need. Just know that the sock itself won't help fight foot fatigue on long days.