In general, the question that you raise is cogent. A sefer Torah has a higher level of kedusha than ordinary sefarim from which we learn, and one may not use an article set aside to serve an object with a certain level of kedusha for something with a lower level of kedusha.[2] Since sifrei Torah are placed on the bima-table, one would expect it to be forbidden to place sefarim of lesser kedusha there. The Mishna Berura[3] says that not only is the table cover upon which the sefer Torah normally sits a tashmish kedusha (an article that is intended to serve an object of kedusha) because of its contact with the sacred scrolls, but so is the table. The reason is that the covering is (partially) removed at times, at which point the sefer sits directly on the table.
Nevertheless, the above is true only when the kedusha is allowed to take full effect. One may make a condition to limit an article’s kedusha and allow its use for additional purposes. A source for this concept is the Yerushalmi,[4] which discusses various items that serve sifrei Torah on/in which mundane things were placed. It explains that a condition can be made from the outset to allow such joint use. Other sources take the matter a step further and indicate that no explicit condition is needed to limit the scope of kedusha in cases in which circumstances indicate an implicit condition. For example, the violation of me’ila (misappropriating property of the Temple) does not apply to the holy garments of the kohanim because the “Torah was not given to angels,” who, unlike humans, could be vigilant to use such garments only for their designated services and not at all beyond that.[5]
The Terumat HaDeshen[6] employs these ideas to explain the common practice of making personal use of articles that serve a sefer Torah. Concerning holy articles that are under the auspices of the community, he argues that we can apply the concept of “lev beit din matneh aleihem” (literally, “the heart of the court makes a condition about them”). In other words, when dealing with matters that affect the masses, in which case it is difficult to avoid the use of the tashmish kedusha for other purposes, the normal “rules of engagement” that enable mundane use can be assumed without stipulation. In contrast, we must be concerned that an individual who owns a holy article may want the full status of kedusha, about which he feels he can be careful.[7] When an individual plans to transfer the article to the community promptly after he obtains it, we presume that he intends to limit the kedusha according to the recipient community’s needs.[8]
One should be aware of a few limitations in applying lev beit din matneh. First, the principle only applies in situations in which it is clear that there is a practice of using the holy article for a lesser kedusha.[9] Even then, the Terumat HaDeshen was not enthusiastic about relying on the leniency. Therefore, it is preferable to state explicitly when donating the article or starting to use it that its kedusha will be limited.[10] In any event, one should not use the holy article in a disgraceful manner.[11] Although lev beit din matneh can allow even mundane uses of the article and the leniency can be quite broad, there are strong indications that the usage of a given article may be permitted only for customary functions, but not in other ways that are conspicuously different.[12]
Returning to your question, the Terumat HaDeshen[13] himself addressed the matter of putting sefarim on the bima and even leaning on it. He said that the widespread practice was acceptable because of lev beit din matneh. Since his time, it does not appear that the practice has become less prevalent. Therefore, one may learn from ordinary sefarim at the bima.