It's not clear what moving all trade to Taiwan would bring in terms of benefits to the Qing. Canton already has trading infrastructure and administrative control over said infrastructure.
I think the idea of 'foreign influence' being the main reason for Qing restrictions on trade is probably overstated. Like all autocratic countries, the Qing was of course worried about the impact of alternative power sources (most notably Christianity) popping up amongst the peasantry, but the fact that Canton existed (and that authorities were not too worried about the large non-Canton smuggling trade) meant that the Qing could certainly live with some level of foreign influence, especially on the merchant level.
The bigger reason for why Qing would want to restrict trade was probably a mercantilist policy that was aimed at maintaining the government's precious metal reserves. A more open policy during the Song, Yuan and early Ming caused China to have a severe balance-of-trade problem, and Ming over-exposure to American silver was an important part of what did the dynasty in during the crucial years of the 1630s-40s.
In this light, Qing policy was probably aimed at maximizing precious metal inflow as much as possible. To do that they would have to create an artificial monopoly over their home-produced goods and fleece foreign traders into trading silver for goods (a well-honed tactic throughout Chinese history). Obviously to do that, you must restrict foreign trade.
So seen in this light, whether trading occurred in Canton or Taiwan wouldn't have technically made much difference to the Qing Dynasty. Of course in reality Canton had all this infrastructure in place, while Taiwan was some sparsely-populated island that wasn't particularly defensible considering Qing's naval weakness, so moving trade there wouldn't have made much sense.