Why do most phono preamps lack XLR input even thought cartridges are naturally balanced?

First, it's a longstanding tradition to offer only RCA inputs.  Second, it is not enough to offer XLR inputs alone, in order to take advantage of the balanced nature of phono cartridges; one would have to introduce a true balanced phono circuit internally.  That requires nearly double the parts count, which increases the cost of building the device, which reduces profits.  Some inherently SE circuits do use a transformer interface between an XLR input and an SE pathway, which does glean some of the benefits of balanced operation.  So, there are some phono stages that do offer XLR inputs and do offer balanced circuitry.  There is no "con" view of balanced designs, unless cost is an object.  I have read the rationale in favor of RCA inputs and SE circuitry, and it usually involves a story about colorations due to added parts count. 

I can see one possible problem with true balanced operation.   Gains of both amplifiers have to be exactly the same, otherwise common mode noise will get converted to normal mode signal.  It requires some form of cross-feedback to keep gains exactly the same.  Phono preamp in addition has RIAA equalization that changes frequency response within audio band by 40dB  (100 times).  I suspect, that it would be very difficult to match it in both "legs" of true balanced phono stage.

What lewm said, regardless of source type.

kijanki, To the degree that signal handling by the two phases of a balanced circuit is not exactly symmetrical, you are correct in saying that will reduce Common Mode Rejection, and it does for sure in tube-based balanced circuits, because exact matching of vacuum tubes is not possible or stable even if it's momentarily possible.  (Your argument about RIAA equalization does not hold as much water as does the argument about tube or transistor gain matching, because it is much easier to exactly match capacitor and resistor values, or to tweak the values for good balance, than to match the gain components.) To all of that I say, so what? CMR is reduced from some perfect value to some lesser value, but you still do get CMR.  Whereas, in an SE circuit, you don't. I have two fully balanced phono stages; neither of these ever drove me crazy with hum and noise problems that I read about all the time in relation to SE phono stages. But the OP asked "why" we don't have (more) balanced phono circuits, and I think it's mainly the profit motive.

As @lewm notes, that a phono preamp has XLR inputs doesn't necessarily mean that it is fully balanced. But the inverse is also true - there are differentially balanced phono preamps that use RCA connectors. ARC Ref Phonos, for example.