Sounds to me like you have taught your bird when she wants to go to her cage to play with her toys and doesnt want to interact, she just has to bite.
Yeah, I suppose that is a possibility, but it didn't work out that way with my birds. To be clear, the vast majority of the time a quick "no biting!" or blow in the face stopped the behaviour right away. It was only when it escalated to "I'm frustrating/hormonal/seeking negative attention right now raaaaa" that I put her in her cage, and that occurred maybe 4-5 times over a 2-3 month span. Since then I have never returned her to her cage for "disciplinary" reasons, and she never bites either, so it didn't translate to a learned behaviour for her.
When I HAVE seen this happen, is with my coworker's lovebird (this guy is mean, very bitey). She will not correct the biting behaviour the first 10 times (in fact she just jerks her hand away and he keeps coming, it's a game to get her attention), and then she gets fed up and puts him in his cage. I do believe that if you curb the behaviour at the first bite or suggestion of a bite (either by saying "no", blowing, tilting or shaking your hand [not the bird

], stopping what YOU are doing that is ticking off your bird, moving away from the bird and into its comfort zone, whatever) you shouldn't have to be putting them away from you (either holding them away from your face, on the floor, perch, or in their cage) very often at all.
Another of the problems that can be created from using a cage as time out. Just because its not *meant* to be a time out doesnt mean the bird sees it that way. Think of a 2 year old. If a 2 year old had a really nice room, plenty of toys and was put in their room for punishment, only to sit for 10 minutes playing with toys, how is that a punishment? If they dont know they did something wrong, then theres no consequences for their negative behavior, thus why most childrens time outs are given in a place away from toys and rewards.
It
is meant to be a time out... for me anyway,
I see a difference between punishment and time out. A time out is like... I'm ordering you to go over there and take a few deep breaths because you can't calm down on your own.
When we got unruly as kids (not being bad per se - like breaking things - but just being annoying, horsing around, yelling, etc and not listening when told to calm down) we were told to go to our rooms for x minutes. We didn't
want to (more, I think, because we were disappointed that we'd upset our parents), but we'd go, read, sit, or whatever, and come out calm with a new frame of mind and ready to do something else. It was neither "yay! time to play with our toys!" nor was "oh nooooo we have been punished!"
We knew it was because we were being bad, because the order to go to our room came after a few warnings (well, I don't remember knowing this when I was 2, but it was clear my younger cousins that they knew).
Im not saying put the bird on the floor and go make dinner. And for some, putting a bird on the floor and walking away isnt an option, nor something they want to do. It's simply my opinion and suggestion.
I know, and I don't think it's wrong. I'm a big proponent of "whatever works" (working within reason, logic, gentleness and kindness, of course). If the floor works, or a perch, or cage, or whatever - it's all more or less the same idea: a physical interruption of the behaviour resulting in a different frame of mind or attitude after a few seconds of cooldown away from the offending creature (the human, lol).
I have also seen the floor not work... My aunt's lovebird is partially clipped but can easily get off the floor. The breeder advised them NOT to put her in the cage when biting to discourage a bite=cage association (I do NOT disagree with this btw - but in my experience it worked for me), and instead to put the bird on the floor. Even if the bird didn't fly to wherever it wanted to go, it didn't curb the HARD nipping (drawing blood). So I told her what my method was which is:
step 1 - light correction ("no", hand tilt, or blow in face)
step 2 (if biting continues) - medium correction (physically removing the bird from your face or whatever - when I did this i held her in my hand which I extended away from me - not tightly... alternatively, place the bird on the table in front of you if it won't be held)
step 3 (if biting escalates) - put in the cage
I will say it worked for her... And I truly don't think that it's because the birds developed a fear reaction or anything. Nothing else in their behaviour changed and they still seemed perfectly happy, busy birds, they just did not bite, or their bites turned into infrequent light nips... Which I suppose some might argue is just as bad but I think that birds are allowed to use their beaks to communicate as long as it's gentle - and they are allowed to reprimand us if we do something stupid.
Ultimately, if you have a better way, use it... and share it... I'm just saying what worked for me and my coworker's bird and my family member, is that system. I am the first one to admit it if I'm wrong, or change my ways if I think I'm doing wrong but I truly believe that this worked for me, and did not damage my birds in any way. YMMV
BTW, sorry for the novel...!