<p>Some relevant facts:  </p>

<ul>
<li>We seem to have four tags related to this discussion: <a href="https://stats.stackexchange.com/questions/tagged/cart" class="post-tag" title="show questions tagged &#39;cart&#39;" rel="tag">cart</a>, <a href="https://stats.stackexchange.com/questions/tagged/decision-trees" class="post-tag" title="show questions tagged &#39;decision-trees&#39;" rel="tag">decision-trees</a>, <a href="https://stats.stackexchange.com/questions/tagged/tree" class="post-tag" title="show questions tagged &#39;tree&#39;" rel="tag">tree</a>, &amp; <a href="https://stats.stackexchange.com/questions/tagged/classification-tree" class="post-tag" title="show questions tagged &#39;classification-tree&#39;" rel="tag">classification-tree</a>.  </li>
<li>At present, <a href="https://stats.stackexchange.com/tags/cart/info"><em>decision-trees</em> &amp; <em>tree</em> are synonyms that automatically map to <em>cart</em></a>.  On the other hand, <a href="https://stats.stackexchange.com/questions/tagged/classification-tree"><em>classification-tree</em> is distinct, but indexes only two threads</a>, one of which is also categorized under <em>cart</em>.  </li>
<li>It's also worth recognizing that <a href="https://meta.stackexchange.com/questions/135466/how-can-you-find-questions-with-ses-search-features-that-have-now-defunct-tags">making a tag a synonym makes it much more difficult to find questions categorized under the old tag, and this problem has not been resolved</a>.  </li>
</ul>

<p>The points you raise are good ones, but I agree with @whuber that it might not be best to change the current pattern of synonyms.  My suggestion would be to edit cart's tag wiki excerpt to indicate more accurately how it ought to be viewed / used by the community.  There is a linguistic <a href="http://en.wikipedia.org/wiki/Metonymy" rel="nofollow noreferrer">phenomenon</a> in English (and probably all languages) whereby the name of a particularly salient member of a category comes to stand for the category as a whole.  (For example, <a href="http://en.wikipedia.org/wiki/Kleenex" rel="nofollow noreferrer">Kleenex</a> is a proprietary / brand name, but is used to indicate any facial tissue.)  I can imagine "cart" coming to be used (perhaps incorrectly) the same way.  </p>
