Can you get a perfect egg from logins?

The random part is what to plan around. The conditions come guaranteed, so this is not a watered-down version of a perfect egg, but you do not pick what hatches out of it. If you are waiting on one specific Aniimo, a login streak is not the reward that delivers it.

It is also not something a single session gets you. You have to come back across multiple days before the egg lands, which is a reason to open the game on days you have no intention of playing properly. Around global launch it stacks with the launch rewards, which hand out eggs including a free Perfect Egg, so an early account can end up with two perfect eggs in hand without spending anything.

The Prismana egg is a separate path

If what you want is a Prismana Aniimo, logins will not produce one on demand. That egg is tied to the Advanced Companion Handbook, which is the premium track, and it unlocks at level 10. The exclusive Prismana egg it gives is not the same egg forever. The specific one varies across seasons and versions, so which Prismana you get depends on when you buy in and work the track up.

Eggs you play for in Egg Heist

Egg Heist is the mode where eggs are the objective rather than the gift. The PvE side runs solo with no partner required, or as a two-player co-op team with a friend. Getting out with anything means the trip back to an escape boat, and that trip is when you are exposed.

A Pathfinder can extract safely, but only after one personal objective is finished: either personally submitting one Aniimo Egg, or personally collecting a set number of Eggshell Coins. That coin threshold is not published in game, and it was cut significantly in the February 4 update, so a safe extraction is cheaper now than it was earlier in the beta.

Not settled: How many days of logging in the perfect egg sits behind is not stated in the reward text, and neither is the pool the random roll draws from.