cultural heritage isn't about preserving the past at the expense of the present day culture. its about retaining cultural memory that gives whatever the present day culture is doing some context. the efforts to create culture devoid of historical context (i'm looking at you, adorno) have failed to offer much to most of those who might receive it. you need that cultural memory in order move - not necessarily forward, but just move, move in any direction. if you don't understand where you are, your chances of going anywhere interesting other than by pure chance are not very good.
when people, when cultures build *objects* to signify things of importance to them (for whatever reason), it tends to follow that if you want to understand them, and thus to some extent, to understand yourself, some kind of appreciation for those objects is necessary. you need cultural heritage to help appreciate those objects, and paradoxically, those objects are part of the same cultural heritage that offers some chance of appreciation.