In college I got deep enough into Prolog to write programs where cuts were required. Later, I got excited about miniKanren. Now I've been looking into constraint programming, and what I didn't understand until recently is that it basically generalizes the Prolog techniques to handle any kind of equation solving / relational search approach. You can do amazing stuff with these systems (e.g. look at HAL http://users.monash.edu/~mbanda/hal/), including write custom search algorithms (consider classic Prolog unification just 1 search strategy on a limited domain).
But I don't think there is any getting around the fact that this stuff gets conceptually harder, as it gets more powerful. The idea of solution sets as potentially infinite relations, rather than functionally determined things, is very powerful but there is an abstraction price.
And to the extent people can wrap their heads around it, there is a "letting go" in not writing programs in the style of deterministic algebraic manipulations. Part of this may reflect a bias, but the magic of delegating solution-finding to an algorithm is also dangerous. Are you comfortable not knowing how many answers there might be if you let the program keep running?
Similarly, consider Prolog's negation as failure. You can't express many formulas that you might like to involving "NOT". Negation is interpreted as a program just not returning anything. There are important reasons for this model, but again, it isn't necessarily as easy a model where NOT can be used freely.
BTW not many people seem to know that Japan had a huge, Manhattan-style program in the 80's. They made Prolog their lower tier.. like their assembly language, or close to it (this was back when people were still thinking different computing platforms needed different hardware). Some people ultimately blamed Prolog for what is generally regarded as the failure of this "fifth generation" project to leapfrog Western tech. But I think Prolog suffered unduly as a result. In fact that project was trying to to a bunch of ambitious things and they all hung on one another. For example, they were trying to make speech the UI, with 80's tech...
All this said I would encourage anyone to explore Prolog, miniKanren, Mercury, Shen or anything of that ilk.