This is true.
I would still try to get the card before you leave the stage because GHQ and bonus don't always drop new cards. Remember that you can explore while a Seduction Battle is running so do that if you need to. If you don't have the stage's SR card, feel free to use a Card Reveal when you see a 5 step up. You will get enough Reveals from events to do this.
You can also do a lot of exploring during Elite Guard because the time to recharge Focus after fighting Elite Guards will be much greater than the time to recharge Stamina after finding Elite Guards (usually). Since exploring uses mostly stamina, just start doing that once all your Focus is gone.
Note that recently the 3-4 day breaks have been shortened to 1 day breaks.
I believe the cutoff is actually level 60 for moe, and it could be as high as level 80. Once you get a Sexy to level 25 via chance time and gacha, you could begin to fill up that card. I have yet to really pay attention to Babes; they are low priority.
Two more things: The first thing I do every day for daily missions is open "Get 3 N cards" and use the N gacha. Once I have gotten 3 N cards, collect the reward and open "Get 2 R cards". Once I have gotten 2 R cards from the N gacha I collect the reward and then begin playing normally, with "3 Chance Time" and "3 Experience" opened.
Finally, once you get to Level 50, DO NOT complete the "achieve level 50" mission. It has to do with the N gacha.
Before completion: If you get a maxed N card, you will get a random level up of a non-maxed card you have. It is usually N, but it could be R or SR. If you max out all your N cards, you will only get levels for your R and SR cards, regardless of what you pick!
After completion: Your cards now go to EX levels and can gain 3 SED per EX level, regardless of rarity. If you get a maxed N card, you get a useless N Wild. Yuck.