You “need” a dental insurance for routine dental treatment by your dentist like a bi-yearly dental check up and simple fillings for cavities. But usually the maximum coverage is only two or three times higher than the premium, which does not make for a very good insurance: Instead of paying a (relatively) low premium for a rare but expensive event (like being hospitalized), most people pay about the same in premiums than they use in dental treatments. And when you need insurance the most (i.e. if you have to get really expensive dental treatment), you are not covered and must shoulder most of the costs yourself.
Dental surgery (were you referred to a specialist within the clinic?) does not require extra insurance and since mandatory health insurance coverage is defined by the law, it's probably not specific to your insurer or mine (the same thing happened to me a few years back). Note that even if you did have to pay more than you expected in this case, the rule is actually to your advantage. You can drop the dental insurance (a bad deal in any case) and still be covered for serious problems like the one you had. Also, if you need some other medical treatment in the same year, you will reach your deductible (eigen risico) quicker.
So it can be a nasty surprise the first time but it's not really an issue that could or should be “solved”, it's just the way it works in the Netherlands.