I did say "may" be unnecessary not definitively is unnecessary. If there is an adequate amount of lipids and sterols already in the wort then the yeast don't need the oxygen as the cells will produce healthy membranes from those in the wort. I don't leave all of the cold break behind in the kettle, I use yeast nutrient and pitch fresh starters. Sometimes I'll throw part of an old pack of dry yeast into the kettle to provide the wort with more nutrients. Combine that with a little rocking the carboy, my yeast likely has everything it needs without me using an O2 wand. Unless the OP has slow or stalled fermentations oxygen is something he or she may not need to worry about.
While I sort of agree.. and it may be good for some ale fermentation's, I don't agree with lager fermentation's. If this was the case then big breweries would just pitch discarded yeast and nutrients into the boil and call it a day. But they don't, and Kunze outlines yeast and aeration in almost a full chapter.
Practices at big breweries do not necessarily translate to the homebrew level. I always pitch a fresh SNS starter, which has been aerated. Big breweries are likely re-pitching yeast from previous batches which would require oxygenation of wort. Some of this is also likely dependent on yeast strain, OG and style, which you mentioned.
I've never had a problem and I won a competition with a lager done this way (I did shake the crap out of the carboy for five minutes on that one LOL). The one time I had a sluggish fermentation was when I repitched a month old slurry into a 1.090 wort but that isn't a normal practice for me.
My practices work well for my system and beer styles. I wouldn't want the OP to go out and spend a lot of money on stuff that isn't necessary. If he or she makes great beer with current practices then investing in an O2 wand and stir plate is just going to be money out of the bank.