Litvishechosid:
Good question. If there was a halacha of kedusha, there would be a more reliable mesora on the location of Har Sinai. There isn’t any. The locations that can be toured today are identified by people who approach the subject as a piece of history, using landmarks from references in various places, mostly psukim from around Tanach. There are also Arab names for various locations around Sinai desert that are suggestive. Yet, none of these constitute mesora. Yes, there were rabbonim that were impressed by the conclusions of these historians, but they did not opt to travel there, and the information was just something interesting. The posuk states clearly that the kedusha from before Matan Torah until after was intense, and it was ossur for human or animal to breach the borders to ascend even a drop. But במשך היובל המה יעלו בהר, implying that this intense kedusha was no longer.
There is a Medrash Tehilim that states that Matan Torah was on Har Hamoriah. It states that a piece of Har Hamoriah was taken and moved to Midbar Sinai, and it became Har Sinai. As is the case with many midrashim, it may help answer certain questions while leaving others unanswered. For instance, כפה עליהם הר כגיגית can refer to the lifting of the mountain above them, which could have been while it was in transit. Yet, they camped around the mountain prior to that. Puzzling. It may be that Har Sinai was restored to its original location, Har Hamoriah, after that, and therefore no one can identify it in the desert with certainty because it just isn’t there.
With all the research, the location in the desert that is most often considered Har Sinai, leaves us with many questions about authenticity. According to the posuk, there was a river/rivulet near the bottom of the mountain, referred to by the מעשה עגל. In the entire region there, there is not a drop of water to be found. I can accept with ease that the blossoming of flowers was temporary, but a body of water should still exist. Even dried river beds can be identified, and no one succeeded in finding that here.
I am with you in recognizing the feeling of kedusha with regards to objects that belonged to tzaddikim, and one would draw a קל וחומר to Har Sinai. The implication from the posuk does not support that, nor does the complete absence of any mesora suggest that there is what to find. My rebbe once commented that this was on purpose, that Torah does not have a physical address, and that one should recognize the מקום תורה as dependent on the study of it, which can be anywhere.