Not necessarily. The term "carburetor problem" covers a lot of territory. If the problem is a misadjusted choke, idle mixture or float level, a simple adjustment may be all that's required to fix the problem. If the choke spring is broken, or an electrically-heated choke housing is not working, either can be replaced without having to replace the entire carburetor. Even if your carburetor has an internal problem such as a bad accelerator pump, clogged jets, bad float, defective power valve or vacuum leak, these too can be corrected by overhauling your carburetor and/or replacing the faulty component.
The fact is, most mechanics today don't want to mess around overhauling carburetors. It's time-consuming, difficult and sometimes requires special tools. It also requires a fair amount of knowledge. And even when it is rebuilt, it sometimes works no better than before because of air leaks past worn throttle shafts or other problems that were either overlooked or not corrected. For this reason, most mechanics would rather replace your old carburetor with a new or remanufactured one. It's a lot easier, faster and the results are usually guaranteed. And, it's expensive. A rebuilt carburetor may run anywhere from $150 to $600 depending on the engine application and complexity of the carburetor. New carburetors are even more expensive. But if your old carburetor has a major problem such as worn throttle shafts, a broken or damaged casting, missing parts or little green gremlins that defy diagnosis, replacement may be your only option.