Taildrop just solve a smaller part of the problem space.
For example, often the target might not be up or connected and you might want to have your file available to all your devices.
The closest competitor to Telegram in term of convenience is email I think.
Just a common use case, I will be at work, and will get a airplane eTicket pdf for a business trip.
I would connect through telegram web to drop it into my saved messages. Then, later I would be quite sure to have it available on any of my phones when being at the airport, and even being able to access it from my personal laptop later for a visa request for example.
Also, a moment later, I could suddenly share it with my girlfriend so that she have all the info to pick me up when I will come back.
In addition I can quite easily search such documents by keywords or date.