As most things, context is everything.
There is rarely 1 answer that is right for every possible scenario.
So, partly depends on the norm for that group. If there’s a history of rotating round houses to eat takeaway and no-one ever cooks, and all always split the bill….fine. Do that.
If there’s a history of people hosting a dinner party and cooking for friends and one chooses instead to get takeaway…probably they pay. They have chosen takeaway instead if the effort if cooking and paying for ingredients. Fine. Do that.
If usually people go out to eat and split the bill and one time, people decide to get takeaway for some kind of practical reason and one person offers to host it, then split the bill. If usually one person pays for all the meals in a restaurant and it’s your turn, then fund the takeaway.
Go with the norm. Usually this means taking turns to pay for everyone or always splitting. This works well for groups who often eat together.
The tricky thing is when it’s a one-off or a first eating together. Then there is no precedent ir norm and you do t know if it will become regular or not. Some people can afford to pay for the group and are happy to do so, and will, even if it is just a one-off and they will never get a return takeaway. Others prefer in that situation to split it so no-one feels they owe anyone else. Finances of the group play a role here. If everyone is young with limited finances, simply paying your own way makes sense. In an affluent older group, one person covering all might not be an issue as the money is a drop in the ocean. Being aware of others and their financial situation is good…because the affluent can make less affluent feel awkward by either hosting and paying ….less affluent feel duty bound to return the favour….or that they can never host, if the norm is host must pay.
Communication upfront helps a lot….as with most things. Uncertainty is what makes people anxious rather than costs themselves. If you know what you’ve been asked to and any financial implications, if you dont like them you can simply politely turn down the invitation. Not knowing causes worry, or finding out that all the guests at your house expect you to fund a takeaway when you’d imagined splitting the bill, can cause all kinds of resentment. Most is solved through communication upfront.
So if inviting or organising a takeaway, make clear if you expect to bill split or to pay. If someone new is joining a group, make clear how funding works in the group. It doesn’t have to be awkward at all.