In VERY broad generalizations that are bound to piss of at least a few people…
The role of the DJ can be seen as an “Artist” or as a “Service Provider”. There are a lot of other ways to view DJing…but focus on the Artist/Service Provider split for now.
Many mobile DJs view themselves more as “service providers” than as “artists.” This means that the mobile DJ is there to play music that their clients (and their guests) will enjoy. To the extent that the DJ approaches that task with some point of view and with their own taste and style, so much the better. Requests are a given, and unless REALLY out of place, should be played.
Many club DJs view themselves more as an “artist” rather than as a “service provider.” The DJ may take their artistic queues from themselves, or from the format of the club…but the DJ is there to put on a show. It may or may not be “their” show. To the extent that the DJ “reads the floor” and “plays for the crowd”, so much the better. Requests may or may not be permitted. In the end the “advertised format” is MORE important in setting the format than requests from the people who show up (e.g. if the club advertises a “techno night” there is no amount of requests that should get a “country” song played).
Neither approach is “better.” There is a lot of fun to be had with both approaches, and money to be made with both approaches. It is important to be comfortable with the approach that you are taking. If you are really not comfortable seeing yourself as a “service provider,” then mobile DJing may not be for you. If you like playing a wiiiiide variety of music across many genres, then club DJing may not be for you.
I am primarily a mobile DJ. I sit in at clubs several times a year for friends…and it takes a LOT of prep work for me to change gears and get into a “single format” mindset for an evening. I enjoy the challenge, the excuse to geek out over music, and the intellectual exercise of crafting a set with those kinds of limits. BUT, it is not something I would enjoy week in and week out. That is an important thing to know about yourself.
Getting back to the OPs comments. You seem to be “down” on Top 40 songs, but you also seem to be largely unfamiliar with the genre. You are early in your DJ career. Try not to rule out whole styles of music before you really get a change to explore them.
There is still a LOT of individual expression that is possible within the “Top 40” genre. I pull from the Top 40 lists going back 2 to 4 to 10 years. I routinely pull in remixes of Top 40 tracks. I have even pulled in acoustic covers of Top 40 songs. AND…I still mix in “other” music that is not Top 40…Classic Rock, EDM, Hip-hop. With most non-EDM genres, there is a wide tempo range to work with…that can be really challenging to mix & blend into a set. There are even “live drummers” on occasion…so you have to pay attention and ride the pitch bend to keep the music in sync. Even in something as “awful” as Top 40, there is more than enough for any DJ to keep themselves (and hopefully the audience) entertained. 