If one assumes a "perfect" carburator, eg, one which produces the proper air/fuel mix at all airflows from idle to maximum, there would be no need for a progressive linkage.
Stock49 is correct; it comes down to air velocity through the carb. This is because carbs are not perfect, and because at idle and off idle, the mixtures are acheived using different mechanisms. The transition from the idle circuit to the main circuit is difficult at best.
With a single carb, one spends little time in the transition stage; normal driving requires some minimum horsepower output, which is above the transition level.
With multiple carbs, however, that minimum horsepower output level (and consequent airflow demand) is now split between multiple carbs forcing all of the carbs to operate for extended time periods at the point where the carb doesn't know if its idling or trying to produce power. Operating within the transition range between idle and main mixture circuits makes the resultant mixture unstable and tough to drive.
Is this a vote for progressive linkage? No. A manifold designed for even air and fuel distribution under WO conditions isn't going to be able to provide balanced distribution under part-throttle conditions. Typically, on an in-line engine, the outer ports run leaner than the center, and this during the output level where one spends considerable driving time. All in addition to the maintenance hassles.
Is this then a vote for non-progressive linkage on multiples? Not neccessarily. While if a driver understands why the carbs stumble at small throttle opening and makes a point of driving in such a fashion that the throttle is either at idle or opened to above the stumble range. This kind of off-on driving will be sure to displease the mother-in-law.
Multiple carbs are a hot-rodding tradition because at the time engines were being tweaked to develop higher power outputs, single carbs capable of delivering the total airflow needed simply did not exist. Multiple carbs to get the total airflow were the only route, and the driveability problems were just accepted as part of the cost for that power.
A larger single carb on a well-balanced manifold is far more likely to provide both the total power and the driveability. If one looks closely at many of the multiple carb setups on hot rods, you will find that many of the carbs are actually dummies... Installed for the look, left disconnected to retain the functionality.
Like the nostalgic look? Consider multiport EFI. Manifold pressure-based EFI systems (Like the GM system) don't care how many throttle bodies are installed, they just care about the total pressure in the manifold. Three two barrel air valves, or six single barrel air valves would retain the look and the functionality.
