Concur with both your views... to an extent. As usual the best path may be a balance.
It is true they are "wildcards" since they do give special advantages & flexibilites however, they are not instant nor free. It takes time & resources that could otherwise be used on somthing else.
Which is why they create 1 more tradeoff decision & THAT is what makes this (or any game) a classic... there are SO MANY different ways to go.... many of which are mutually exclusive.
On the other hand they may be OVERDONE in their exclusivity & power.
Keeping in mind real world programming constraints + continuing what is possible of the 3rd generation of this Classic:
I suggest either a few MORE to spread around or/&
adjusting present one's time of effectiveness both +/-.
Another alternative would be to have somthing like a "1st & 2nd place reward"...
1st civ the achieved it got full power, but rather than stop everything & TOTALLY screw others that were rushing for that wonder...
2nd place would get a reduced level of benefit from it... for the same cost, however.
THINK that thru to all the tradeoff's alternatives, fairness, interest level that could increase?!
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"Hm-m-m, doubt me you will?"