You raise a good point (at least in regard to a serious type of leaning) – albeit one we did not overlook, but rather chose not to address. If the matter were as clear cut as you perceive, it would present problems in most shuls, and not only for a person getting an aliya. Gabbaim often lean on the shulchan, and objects, including tzedaka boxes and sefarim, are routinely placed on it. Let us evaluate if all of these practices are really forbidden.
It is not clear that the shulchan has a status of a tashmish kedusha. The gemara[4] cites Rava as saying that he at one point did not think that a shulchan has a status of tashmish kedusha. Since it is covered with a mitpachat,[5] which is what comes in direct contact with the sefer Torah, the shulchan is ostensibly only a tashmish d’tashmish – that is, it supports the mitpachat upon which the sefer Torah sits. Rava concludes, however, that since the mitpachat is sometimes removed and the Torah then sits directly on the shulchan, it is indeed a tashmish kedusha. The status thus depends on whether or not the shulchan is consistently covered. Either way, this does not really answer your question, as regardless of the status of the shulchan itself, it should be forbidden to lean or place extraneous objects on the mitpachat.
The Beit Yosef[6] cites the Mordechai, who says that it is worthwhile to make a condition initially that the mitpachat will not receive the type of kedusha that would make it forbidden to lean on. He proves that if this is not done, it would even be forbidden to put sefarim on top of it, since they have a lower level of kedusha than the sefer Torah does. The ability to make such a condition is confirmed clearly by the Yerushalmi.[7]
The Rama[8] goes a step further, ruling that (at least in shul[9]) it is not necessary to make a condition. Because it is evident that people will have trouble refraining from leaning or putting things on the shulchan and/or its mitpachat, there is an implicit public condition (lev beit din matneh) protecting them from possible wrongdoing. The concept of lev beit din matneh is found in the gemara[10] regarding objects that were given for the Beit HaMikdash and its service, and it has been applied to many cases of holy objects.[11] The condition does not allow one to use these objects in an unseemly manner,[12] but that does not seem to be a common occurrence.
Admittedly, the Bi’ur Halacha[13] suggests that lev beit din matneh applies only to those practices that are difficult to avoid. However, given people’s habits and limitations, it is difficult to expect everyone in shul, whether having an aliya or not, to make sure not to lean on the shulchan when standing near it during a variety of different activities. Nevertheless, if one can easily avoid the issue, it is proper that he do so. It is apparently for this reason that several Acharonim[14] suggest that if one is very overweight or weak, and he therefore needs to lean significantly on the shulchan, he should pull back the mitpachat and lean on the surface of the shulchan.
Since it is rare for someone to lean on the shulchan intentionally and it is often not feasible to pull back the mitpachat, we purposely omitted this discussion in our original response. As explained above, being careful not to lean is apparently not fully required and is seldom practiced, in our experience. .