Is it necessary to practice long notes on the saxophone?

There's nothing WRONG with using ballads for tone practice, but there are two ways in which it's not as good as specific tone practice.

1) Very few ballads cover every single note in the entire key range of the horn from low Bb to as high as you can play altissimo. No ballads involve the complete range of dynamics from pppp to ffff unless of course you specifically do something about this. Every note, and every dynamic level, is a little different in its response.

2) No matter how you play with the time, you'll still be constrained by the song's form to moving from one note to the next to keep the song going. So if you need to go back to that low F#, you probably won't.

My particular tone practice consists of playing each note on the saxophone from low Bb to the highest altissimo I have, starting at pppp, crescending to fffff, then back down to pppp. If the note drops out when very soft, or breaks up when very loud, I go back and try it again. On the lower notes of baritone, I'll need to take each note in a couple of breaths. One of the objectives is to increase dynamic range. If you are regularly practicing going from too soft to too loud and back again, while trying to maintain a constant tone quality and a constant pitch, over time the soft and loud dynamic levels at which you can play with a pleasing tone in tune will get softer and louder. The wider the range of "just barely in control", the wider the range of "in pretty good control" will be, and the wider the range of "command of the instrument with complete control of expressive qualities" will be. (This applies to range as well; someone who's spent several hundred hours concentrating on starting low Bb at pppp level, or playing high F in the palm keys at ffff without having the reed close up, willl have a far better control of these extremes of tessitura.)

And the last point: I recommend that tone exercises be done, whenever possible, outdoors in a location far away from reflective surfaces. This helps build a big husky tone with vibrancy. Avoid practice room tone.

Since I'm the one who wrote the most lengthy post on the pro-long-tones side, I'd like to clarify:

I did NOT say you can't build tone through other means than long tones. I would like to suggest, though, that other things mentioned here do not provide the CONCENTRATION on tone quality that practicing JUST that will do. You do all realize that professional athletes almost uniformly spend time in the gym working on strength, flexibility, and aerobic capacity? Even though the game of American football does NOT involve lifting weights, nor the striking of yoga poses, nor the running of long distances rather than sprints, I can guarantee you that all successful NFL players stretch, they all spend time in the weight room, and they all run laps.

We practice to get better at things. Practice that's concentrated on a specific item is generally more effective for that item than diffuse practice. You need multiple things to be covered in practice, of course. That's why we practice scales; that's why we have etudes; that's why we (many of us) practice overtones; and if you choose to use long tones (there are several different ways to do this), you'll be spending that time concentrating purely on airstream, voicing, embouchure, and the resulting pitch and timbre. You won't be spending any of your attention on fingering, on changing notes cleanly, on expression, on vibrato, on improvisation, on remembering the melody, on reading the notes. You'll need to practice those things elsewhere. And of course you'll need to practice putting it all together, by performing repertoire.

There are as many practice regimens as there are musicians, but I always come back to the proposition that the standard pedagogical methods are generally the fastest most efficient way for most people to get up to speed and/or maintain themselves at a high pitch of performance.

It's not that the examples of singers (and I didn't spend a lot of time thinking of specific examples, to be honest) were formally taught, but rather that they learned the techniques, whether on their own or by instruction. Good deep diaphragmatic breaths, open air ways, proper projection, etc. Dylan sings through his nose with what's really a rather unpleasant tone; it fits his performance persona, it works for him, but it's an extremely idiosyncratic way to sing. Eilish needs to take about four cups of coffee and breathe. That creaky half asleep thing has a temporary vogue, but it's not an impressive vocal tone. I find nothing compelling about the sound. It may well fit HER performance persona of the bored alienated teenager.

Moving back to the saxophone, it's pretty easy for someone who has a full command of the production of saxophone tone, to choose to play with a pinched tone narrow dynamic range inaccurate vibrato and avoid the extremes of range. It's not so easy for someone whose only tools are the pinched tone narrow dynamic range inaccurate vibrato and has to avoid the extremes of range, to do otherwise and play over the full range of the horn with a wide dynamic range, rich compelling tone, accurate and appropriate vibrato, and flexible timbre.

Getting back to the prescription of exercises, I continue to believe that for the majority of people, subject-specific exercises are the most efficient way to master and maintain mastery of a subject. Long tones specifically target tone timbre dynamic range and pitch over the full range of the horn. Can you develop these by other means? Absolutely! I'm just offering that in my opinion and the opinion of pretty much every professional instructor of saxophone, the long tones exercises are an effective efficient way to get there.