Because they were afraid Willem III would turn into a king. The regents of Amsterdam liked that they ruled the country and didn't want the stadholder to become the ruler. Even when Willem III became stadholder the regents were some of the most powerful people in the country.
And indeed, the position of Stadtholder wasn't hereditary nor necessarily present. Between the early death of Willem II and 1672 (Willem III's younger years!) there was none, and quite a lot of people in high places would have liked nothing more than a return to that.
And Amsterdam officials and similar-minded were very protective of the powers of cities, often in direct conflict with the Stadtholders (and with at least some tension the rest of the time). Considering practically every Stadtholder after William the Silent purged every major's administration soon into their rule (and quite violently in the case of 1672!), it's not very surprising.
Gelre was itself an interesting case, politically. While the always-Orangist nobility controlled half the Estates, the other half wasn't dominated by cities but also had room for commoners to be represented as a third party. Well, I say commoners, they were guildsmen and militiamen (so obviously they had some means), but they were still not members of the political ruling class.
Jonathan Israel's
The Dutch Republic: Its Rise, Greatness and Fall, 1477–1806 devotes quite a bit of attention to this conflict between the cities and the Stadtholders, as well as earlier and later iterations of that conflict. I'd recommend it to everyone interested.
I don't think so. He was after all already Prince of Orange, count of Lingen and Moers, Baron of Breda and various other titles I am too lazy to look up. Being Duke of Gelderland probably would add a lot (although technically duke is a higher title than prince, it often was't consider to be so in this case).
Burggraaf of Veere and Flushing was another important title, but for domestic reasons. (ie. he basically was the nobility portion of the Estates of Zeeland).
Something that's interesting to consider is that just before his death the States-General were discussing to give William the Silent their respective titles (since times where rough and the Estates deemed centralised stable leadership important, just like Guelders in 1675); a discussion that still lingered on 90 years later when this issue with Guelders was happening. It's what might have happened if William the Silent had survived his assassination, which would form an interesting starting point for a TL.
(I've already sketched something out myself, but it might be a bit wankish; at some point Frederik Hendrik marries the ATL only daughter of John William of Cleves(!))