Not with PADI. OW only included a short introduction to using a compass.
After my wife and I completed our PADI open water last year, we felt less than adequate in really any skills including buoyancy. Our navigation was horrible. We went to one of our favorite spots that had a compass course to work on it. We first just focused on keeping our heading. with 20-30 feet visibility, we were able to find what we were looking for. After we got the hang of keeping our heading we started working on counting/timing our kick cycles. This really helps when you have a bit of a swim to your destination since you have a general idea of how far you traveled. Before that, it was just a guessing game and there were times we would either completely overshoot our destination or we turned around thinking we missed it. One thing to keep in mind is you may need to reevaluate your kick cycle as you progress. My kicks were really inefficient originally. Further, I mainly flutter kicked when I started but now I mainly use a frog kick.
OW really doesn't teach you kick styles either. I think those were part of the AOW and PFB.
Please note my use of the word "should"! "Should" is a dangerous word, after all, I
should not have to pay so much in taxes. I
should be paid more! And so on!
Now about standards. Yes no agency that I know of (I've taught for PADI, SSI, and SDI, so I'm by no means an expert of all agencies, though I do collect as many standards from different agencies as I can) teaches kick cycles/times swims and/or SACs in open water. SDI (and NAUI, possibly others) do allow an instructor to require it as part of that course. I followed the example of other SDI instructors who do include both items to enable new divers to basically plan along the lines that are in the dive planning document found in that folder link I provided. Nothing in that document is earth shattering or new. It is simply the collection of fundamentals to give new divers the skills to overplan, as no one is going to figure out how much gas they will have on such a strict plan. However, going through that exercise once or twice gives new divers the confidence and skills to plan and execute dives in similar conditions to which they were trained. They are not as nervous as they execute their dives and see "hey, I have about as much gas as I thought I would by this point. Everything is fine." Eventually they'll have a sixth sense of their expected gas consumption as they conduct dives. Only when they get into technical diving would they get back to meticulous dive planning.
Some instructors don't like that document, seeing it as impractical as it takes more time. But others love it as it is thorough. The people who like it tend to teach in more challenging conditions (cold water, currents, bad viz).
Unfortunately, no mainstream agency in the WRSTC prohibits instructors from placing students on their knees. RAID does require that to meet performance requirements, skills must be performed neutrally buoyant. That's a big step in the right direction. No agency prohibits an instructor from teaching their entire course neutrally buoyant and trim, but unfortunately not all instructors take advantage of that allowance.
I'm sorry you had a less than stellar experience with your open water. I didn't realize the number of standards violations occurred in my open water class until I became an instructor. People in general, myself included in the beginning but no longer, place faith in instructors to teach everything they are supposed to at a quality level. I'd also suggest zeroing in on correct weighting: the absolute minimum required to keep you from corking to the surface at your shallowest stop (5 m / 15 feet for safety stops) with an empty BCD/dry suit with a nearly empty cylinder (35 bar / 500 psi).
But I disagree about finning. You should (there's that word again) per PADI standards be able to reasonably flutter kick at a minimum. I.e., no bicycle kicking.