Mike, the problem with using concert F (which is the alto's D) to tune Eb saxophones is this: One must either tune to low D (D1) which is flat on many altos, D2, which is notably sharp on many altos, or D3, which might be anywhere. Palm key pitches are very sensitive to mouthpiece variations and pad opening, which might or might not be correct.
Aside, I have spent many, many hours over the years charting intonation tendencies on various saxes on each note, experimenting with pad openings, optimizing intonation on instruments... yes, sometimes it IS the horn. So, I have a basis for my statement a few posts above.
If the player tunes the low D, which is usually slightly flat, all the other notes on the instrument will be sharp.
Usually the player will chose to tune his D2. Since that note is a sharp note, if he tunes that note, the rest of the notes on the alto sax will all be flat. Also, any tuning done with that long note will require excessive movement of the mouthpiece. It is an exercise infutility.
After the alto player goes through the charade of pretending to tune his D, and the band is actually playing, it will be necessary to put the mouthpiece back to where it should be to tune to concert Bb or A (G or F#).
Tuning to concert F is like teaching a pig to sing, it is a waste of time and annoys the pig.
These problems are unrelated to the skill, ear training, or embouchure of the player. These problems come from attempting to tune the alto saxophone using the worst notes on that instument.
You want to tune the alto? Tune the alto's B to concert D. You will be using a note that is good in both octaves. You are tuning a relatively short length of tubing, can set the mouthpiece on the cork precisely. The rest of the horn will fall very close, with minimal tuning problems.
For the tenor, tune it's C to conert Bb, or it's B to concert A, for the same reasons as above.
Now, instead of contending with one note that is in tune (the alto's D) and a lot of flat notes that are difficult to lip up, the player can play most of the notes centered, in good tune, and only worry about D2, which he lips down slightly, or adds the low B key, and for a sustained low D, he adds the C# key. Just two problem notes, easily brought into tune.
And band directors, TUNE TO A=440 reference! The instruments are made to tune to that pitch.