@Nikos.Kyrm From my understanding the performance is similiar. All three have milliseconds latency while archive has hours due to rehydration. Hot has 99.9% availability while cool and cold has 99%
You need to beware of the increased cost of writes and reads of cool. I have not looked at cold, but prices for write/read would be higher from here.
If you store and read 1 TB from cool, Total cost is the same pr month as store and read 1 TB from Hot.
Aux copies/sfulls and restores will increase read and data retrival costs.
Hot gives you predictable costs, while cold can give you varying costs (potentially higher than hot). I assume this is the main reason for recommending primary copy on hot tier. Not a technical limitation.