This question is not specific to saxophone. Anyone who has learned an instrument has run into the question of ‘Are exercises necessary, or can I learn to play well without them?’
Strictly speaking, exercises are not necessary to play at a high level, but they are very helpful. To play at a high level, you need to be able to practice specific techniques and ideas until you don’t have to think about them. These techniques are used in songs. So you can learn them by playing the songs that include them. But usually, the songs only use the techinique for a short section. If you don’t already know how to do the technique well, you’ll have to spend a lot of extra time on that section of the song. In fact, it’ll practically become an exercise. So if you are looking for a way to get the benefit of doing scales without actually playing scales, then find a simple song with lots of runs covering all the notes in a scale in sequence, and play that song in each key you want to practice. I’d rather play the scales, but I know plenty of people on both sides of the fence.
Here’s some thoughts to make the exercises more interesting.
1) Play mindfully. When you are working on exercises, before you even start playing, ask yourself what you want to get out of playing the exercise. Then focus on learning that while you play.
2) Vary the exercise. If the exercise is written as straight quarter notes, try slurring the notes in pairs, or in some other rhythm. Or play them with a swing rhythm. Or see how fast you can play it (use a metronome for that, to track your speed and keep yourself steady). Or try to play it all in one breathe. The possibilities are endless, once you start looking at the written notes as a starting place, rather than an endpoint.
3) Find relevant exercises. If you can’t find them in a book of exercises, then find a challenging song, and take an especially hard measure or two. Think about what makes it hard for you (Fingering? Rhythm? Jumping a large interval?). Then play that measure, concentrating on improving the hard part. If you can’t play it yet, look around for exercises focusing on this problem. You’ll know exactly why you’re doing the exercise, and when you improve, you’ve already got a song which will show off you improvements. This is coming at 1) from a different direction.
4) Decide on 1 or 2 exercises you want to do that day, then set a timer for 10 minutes. Work on playing those exercises as best you can for those 10 minutes. Really listen to yourself, and make sure you are playing with the best sound you can, the best rhythm, the best technique. If you think you’ve mastered the exercise, go back to my suggestions 1 and 2.
Whatever you do, if you find yourself so bored you're thinking of quitting, look for a different way to reach your goal. Experiment with what works for you. Personally, I love exercises, and some days never get around to playing actual songs.