A simple team task with a single team resource; yet in reality many actual team contributions - can it be done?

Question

What people would like to be able to do is to plan for a task in MSP to be done by a team. We plan how much work is involved and the duration.
Any number of team members can be involved in the task. As things delay and get put on hold we may have entire teams jumping in to complete tasks so utilisation is maximised. PMs do not want to open an plan every half hour to add extra resources to
plans
Can this be done in MSP in an elegant way?
What I am currently doing is asking PMs to assign all 20 generic team resources to a task; so any of the 20 team members can assign themselves to the task in the TimeSheet. (In fact they get templates with this setup: there is a join project team task with
every generic team resource added so they can swap themselves into the plan)
Obviously the PMs are aghast that Project server will not let you assign a single team resource and then allow anyone in the team to join in. Am I correct in thinking Project Server will not allow this.
(Project server 2010 - on premise)
Trying to stop the swap to Salesforce - but the errors keep a coming

Answer 1

Yeah the capacity planning is mathematically fine if I know the cumulative total of work across a duration - project just flattens it across however many resources are assigned.
To max utilisation resources can and will be shunted onto projects; in a week they can be put onto 20 projects to fill out the utilisation if a big project suffers a major delay. The PMs cannot spend the time rescheduling 10 plans. The resource want
to easily record time sheeted data against the projects they worked on in the past days.
Whilst "add to task" works and they all know how to use it; it only lists the projects they are a Published resource on. Even being reassigned onto a team task will not help. i.e. if I set up tasks on each and every template with the 20 spare generic
team resources on; if a team resource grabs that 1 task to be assigned - the PM must
1. accept the reassignment;
2. Open and Publish the plan; only then can that resource add themselves to a task in the plan - PMs can't spend time doing this 20 times per project!
I don't really want every resource seeing every project in the "add to task" list - but it looks like this is what I will have to do as the team tasks seems broken in many, many places.
However we already do it for support projects; everyone (who may contribute at any point to a support item) is assigned to an initial task - this makes the project list unwieldy in Add task or new task and adds clutter for the user
Trying to stop the swap to Salesforce - but the errors keep a coming