My basic answer was that the prohibition against worked stone altars follows immediately upon the prohibition against making idols. The whole idea that we can construct for ourselves something holy and supernatural is being critiqued in this law.
But more generally, I noted a trend toward preserving very old ways in the religious function of society, thus allowing society to progress without losing its primitive connection to God. Some obvious examples would include:
the Roman Flamen Dialis (priest of Jupiter) having a diet restricted to primitive cereals and being forced to wear primitive garments, both diet and clothing having been superseded in Roman usage long before;
many ancient societies restricting their priests from using iron tools, iron being a "modern" development;
us still ceremoniously lighting candles in worship, when we have had electric lights for a whole century;
and, of course, the alb I wear dates from the late Roman Empire, when it was ordinary "business dress" for Roman men (the Reformation brought in the academic gown, which was at that time street dress for academics but is now a relic brought out only for religious or academic ceremonial).
This same conservatism can be seen in funeral practices. Weddings are often trendy, but funerals are downright anachronistic, because the grieving family wants to "do everything like it was for Grandma" because that brings them the comfort of perceived stability.
We do a lot of things in very old-fashioned ways. That doesn't make them holier, but it helps us by connecting us to our social or family or personal history and the time when we covenanted with God.