Girl Scout leader here - have led girls Brownies through Cadettes (middle schoolers.)
First, every troop is different. The leader does have the flexibility in GS to run the troop this way, and how we experienced GS as kids is not necessarily how any leader has to run a troop today. But yes, what she's asking is a bit unusual in my experience -- NOT the part of asking parents to lead some activities and provide some materials, though; however, the part of having a parent present for each girl at every meeting is unusual.
It is indeed done by some leaders to have parents take turns leading some (but not all) activities. I have not done it but I've known of troops where parents were asked to each lead one badge during the school year, or just one badge activity, or help the leader chaperone one field trip (local firehouse, local library, etc.) -- though the parents were not expected to be at every meeting, all year long. Regarding materials, parents should not pay for everything (each family should be expected to pay annual dues that the troop itself sets, which helps cover costs like materials), but yes, parents can be asked to pitch in some things, much as a room parent sometimes asks parents to contribute items for a class event. If you wouldn't balk at being asked to provide cups and napkins for a class party, it shouldn't be an issue to provide the snack one week for a GS meeting, or to bring one craft item.
If by "lead activities" you mean that you're being asked to take on one activity a year, or even lead one badge completely or in part, that's not very usual but also not unheard of. And here's one thing to consider: It does allow your girl to see YOU in a leadership position, and to see you supporting her whole troop.
However, having all the girls' parents present at EVERY single meeting is not a good idea.
In Daisies (kindergarten and first graders) it's not completely unusual for parents to stay or for a couple of parents to sign up to help with meetings on a rotating basis, but Brownies are slightly older, second and third graders, and should not need every single parent present by their sides.
Which makes me wonder: Is this leader a brand new leader just starting the job this year? If so, please cut her a little slack; she may be feeling a bit intimidated by the position so she decided from the start that she'd just have every kid plus a parent there, in case any girl had issues or kids didn't get along. The kid management aspect of meetings can be intimidating if a leader has never had to ensure that a whole group of little girls behave nicely toward each other and don't devolve into just running around, not listening. That might explain this arrangement, if she's a new leader and very unsure of herself handling a group of kids rather than just her own daughter. (I'm figuring here that the leader has a daughter of her own in the troop --is that right?)
Bear in mind that this mom is 100 percent volunteering here, and giving her own time to do this. Please approach this in a "How can I help you out here" mode, and try to get other parents to do the same. If this woman is the sole leader, she may be a bit overwhelmed with the idea of being responsible for planning a meeting, buying supplies for activities and crafts, being in charge of behavior, ensuring the meeting space gets cleaned up, ensuring she has the many forms and permissions etc. that GS requires done properly, and, frankly, handling parents' questions and issues. Can you see why she might be concerned if she's new to all that?
Go to her when the kids are not around. Don't do it when she's got the troop there buzzing around her. Ask her if she would consider, rather than having a parent per kid there every time, having a schedule or roster of parent helpers who sign up for helping on specific meeting dates. Suggest that maybe she could have two parents per meeting present so that girls get the experience of being dropped off (which by second and third grades should not be an issue) and the experience of working with adults who aren't their moms. You can also pitch the idea that a roster would let parents get to know other girls in the troop, not just be next to their own daughters each time.
Then, most important of all, please volunteer yourself to set up that roster rather than expecting her to add that to her plate! E-mail makes it easy. She will probably be very grateful.
It might help if you have another parent with you. But don't let the leader feel ganged up on by having a group of you telling her "We didn't sign up for this" all at once. If you frame it more as "We'd like our daughters to get experience in doing things without a parent there and having to follow other adults, but we definitely want to help regularly" you may just relieve her hugely.
But if she says, "No thanks, this is how I want to organize the troop," there may not be much you can do, and you might stick with the troop this year and find another one (please don't leave GS over this! there are other troops run differently) next fall. It is her prerogative though it's not a very efficient way to run things; however, she might get more comfortable with leading a group and drop the "every parent at every meeting" thing by next year, or even later this year.