While you asked about pro/con of more children, I am going to take a step back and puzzle something out of the arguments you presented.
Note that your arguments are either very logical (bigger house, more money) or a little constructed (as someone pointed out - age gap and time to kids doesn't really work like that).
A side note: One thing you have not pointed out is that doctors recommends 2 years at least between kids to give the woman's body time to recover. While you are very young, your wife has been through 3 pregnancies already, and you may gently want to point out to her that waiting a bit might be good for her health.
Your wife's main arguments are more emotional: She feels she is missing something, and she wants a big family.
I think there are 2 issues here:
How big a family do you want?
not right now, but eventually. Do you never want any more kids? Do you want to wait? How big is big for her? For me 3 children is a big family, for some people it is 6 or more!
You should discuss this in general, if you can, besides any discussion on when and how.
You wife is missing something
I think this is the MOST important thing you said in your question. Something is making your wife unhappy, and she is trying to change that.
As a woman, when you have a baby, a lot of hormones gets changed around. Sometimes it results in post-partum depression. Sometimes holding your new baby gives you an intense feeling of joy and happiness. Maybe your wife is missing that? Maybe she was less happy with the 3rd that the first 2, and wants to 'fix' it?
It may also be that after having 3 kids so young, she defines herself as a mother, more than anything else and is worried about what to do as your older kids gain independence.
Maybe she is afraid of going back to work? Maybe she has doubts about her worth except having kids (this is common! And in our culture there is an emphasis on women with children FIRST being moms, then something else, whereas men with children FIRST are something else (teacher, engineer) then dads).
It might be something else completely, but it sounds to me that having another kid is what she sees as a solution - but neither her nor you know what the actual problem is.
I would try to address that (maybe with help of a therapist, if it comes to that) before going to a solution. Be careful not to come off as patronizing, or superior when doing this, and maybe you shouldn't even mention it in connection with the possible family expansion. It is about hers (and yours too) happiness in broader sense of things.