The truly funny part of the idea that the South seceded over taxation (besides the fact that almost nobody in the South said so at the time) is that had secession been successful the South (and North) would almost certainly have both had to impose much greater taxes on their citizens.
Even if the US had allowed the CSA to withdraw peacefully, there were still infinite sources of conflict: borders, trade, fugitive slaves, territories, etc. Almost certainly both sides would have felt obliged to maintain much heavier military forces than those of the pre-1860 US Army. It is entirely likely a European-style arms race would have developed.
It seems pretty unlikely, also, that the South would have been willing to leave its coasts open to blockade by the absence of a navy.
Armies and navies are very expensive and must be paid for. The South would probably have had to raise its tariff much higher than that of 1860 to pay for all this.
The CSA put in place a provision in its Constitution prohibiting protective tariffs, but again it seems likely this would have been repealed or circumvented in short order. Surely the CSA would have wanted armaments that were domestically produced, not produced by its potential enemy or subject to blockade. In fact, that’s exactly what it did during the war, generally quite successfully
So if secession had been successful, within a short time the CSA would have had higher taxes than under the Union, and a protective tariff or its equivalent to boot. Then Alabama and Texas could have gotten their panties all bunched up about Virginia and Tennessee making all the money off the government-supported protected industries.