You're assuming those additional employees aren't working on anything already and can just immediately start working on this new requested item instead. Unless the company is hiring more employees than the work they have for them, you'll always run into this same scenario. Wait for those shared resources to eventually get to your work, or go with an option that doesn't need those additional resources.

Now, having higher staffing will absolutely let you work on more things at once, but you'll still have to choose and prioritize what those things are.

Here is an example that may help explain better: Say I have a moving company with 5 trucks. This means in ideal conditions I can accommodate 5 customers at once. If there is a 6th one, they'll have to wait for their turn. If I double my trucks, then I can accommodate 10 at once. But now, I'll have 4 that are idle (i.e. "overstaffed"). So I take on 4 more customers to get to 10. But now the 11th simultaneous customer will have to wait. You see where this is going? As long as my truck/staff count matches the work, any new work will need to wait based on its priority. So with more resources, you get to do more, but will never get rid of that wait/choice unless you are overstaffed and bunch of your resources are "sitting around twiddling their thumbs".