That's because you are not buying the right ones. Real biodegradable & flushable wipes are okay for waste treatment plants. You need to purchase those that do not contain any trace of plastic fibers.

If you are so worried about clogging anything, put them in the compost bin.

What? You can't say "no" to an entire line of products. Simply make sure that you buy wipes that are flushable AND biodegradable. Flushable simply means that the wipe will make it out of your home. You also need to live in a country where there are rules in place stopping manufacturer from lying on the packets.

If they are made of, let's say, viscose rayon which is wood pulp (well, any compatible plant fiber) there's no reason why it would clog anything at the processing plant.

Edit: Well, it would also depend on how your local plant processes waste. Give them a call and ask them.