If you were to do the TDI sequence in order, you would not begin learning any decompression until you reached the third class; with PADI you start that right away.
That seems a bit disingenuous. Intro is not a prerequisite to anything. And, as you yourself observed later, AN and DP are pretty much always taught together. When I took it, Intro was also included as part of the same class. So, in real life, if you go with TDI, you not only start learning about deco in the first class, you are certified for unlimited deco, 100% O2, and 45m/150' depth after that first class.
And, in fact, you can include Helitrox in that class as well(*). I.e. one class that nets you Intro, AN, DP, and Helitrox. So, after your first class you can do unlimited deco, use 100% O2, AND use up to 20% Helium, with a max depth of 45m/150'. My read of the standards is that the required # of dives (6) is the same, whether it's only AN/DP or all 4 things combined. So it is legitimately just one class, too. Not multiple classes simply taught serially.
*as long as you have Nitrox, Advanced with Deep specialty, and 50 dives.
From my perspective from gas management and deco gas management point it's from gas logistics point of view no longer a 1 stage dive. My gas consumption is reasonable but I would need without thinking about min gas almost a full double 80cft set to make that dive... on deco if you account for a lost deco gas scenario (so deco reserves for your buddy) you are cutting it quite slim for that kind of deco time on 1 deco stage.
So while I obviously don't know all the details of your dive... I don't think it's a great example to make because more prudent divers would probably calculate that dive as a multi stage dive, which is definitely not TDI AN/DP curriculum. *
PS: I did a TDI AN class in 2006, and at least at that time it definitely was limited deco on a deco gas (remember 15 minutes of accelerated deco).
For the record, that dive was me with double 120s and my buddy with double 100s. So, ample back gas. We each had an AL80 of EAN80 for deco. Per our training (my buddy was trained by the same instructor as I was), we planned our deco gas using conservative SAC rates and such that each of us needed well less than half the cylinder of deco gas we were carrying. So, if I lost my deco gas, he would share his and vice versa. We both felt like we were being reasonably conservative (no, not super conservative - we didn't feel like the anticipated dive conditions warranted being super conservative - warm water, decent viz, little current, no penetration, not a huge wreck site) in our gas planning and that we would have no problem accommodating a scenario where either one of us lost our deco gas. We had enough back gas in reserve that either one of us could have finished deco (on 80%) left the other breathing back gas, gone up to the boat, retrieved another cylinder of 80% (of which we had 3 extra 40s, in addition to the 80 we were each carrying), and brought it back down. But, since we were both carrying more than twice what either of us needed, that was an extremely remote possibility. And, in fact, we both got out with WELL over half our deco gas remaining. The only way we would have needed help from someone else is if we both lost our deco gas (or both lost our back gas).
I don't think our plan was imprudent. I do agree it would have had a shorter runtime if we had been able to employ 2 deco gases. But, neither of us were trained for that, so we maximized the usage of our training without exceeding it. Also, as I said, AN/DP standards do allow for the instructor to teach use of multiple deco gases. Our instructor simply chooses not to.
When you did TDI AN, did you also do TDI DP? Regardless, it does sound like the curriculum and standards have changed sometime in the last 11 years. I guess that's to be expected.
