The argument in the aforementioned silly article was that humans spend most of their life standing on only one foot, like when walking. I think you have beaten that nonspecific-training horse to death though.
Also, "stabilizing muscles." - in particular I got the lunges notion into my head while looking at the T Nation "neanderthal no more" series searching for accessory movements to speed along my posture improvement. I know, I know... Just deadlift whatever the female equivalent of 300lbs is before I complain about posture...
At the risk of sounding sexist, lunges are to display the derriere's of the ladies. They have no value beyond that. As to the OP being sore, I'm surprised no one has commented, get your squat to even 315lbs and then try again. Lunges are like a break from the real work... In addition, any Globo gym trainer can find something silly to make you sore, but few can actually make you strong.
The people who recommend lunges are the same ones who feel that soreness is a sign of effective exercise. It's definitely not training.
Back in the day before I knew better, I would use walking lunges as a "corrective measure" for groups of candidates on military courses. Every time they sat down or climbed stairs they would be reminded about what they had screwed up and that they shouldn't do it again. I did a lot of them in my normal routine so I was adapted to the volume and it did not hurt me that much.
The older and (slightly) more mature version me now knows that that was stupid.
I would recommend just dropping them altogether, since they have to be done with really light weights or else you just fall over and the only way to really progress them is to jack up the volume which creates soreness.
I'm a female, and thought I'd heard the female NLP for squats tops out around 150-175. Not that I don't have plenty of room for improvement, but I am definitely in need of light days and thought I could perhaps afford to play around with some "fun" stuff.
Also as said female, I wouldn't be opposed to improvements to my derriere, but it's hard to imagine anything being more effective for the booty gains than the standard squats and deadlifts. My hip size went up 4 inches with no appreciable change in body fat or waist size. Although, the constant need for larger pants is... Expensive.
Lunges just aren't that great. They make you sore as shit, they can't be loaded that heavy, and they produce a large moment arm on the knee. I understand the desire to mix in some light stuff, but I would find something else that's fun if you really need it: front squats, light squats, dynamic effort squats, box squats, good mornings, etc. There are a ton of options from which you can sample if you really feel the need to mix it up.
Personally, I think light squats are the best for a light day that needs a "squat" slot. Nothing says "fun" like being done with your workout in 40 minutes when your volume day takes 90-120 minutes.
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The "perfect fill-in-the-blank day" videos is what made me stop listening to him. In one breath and video he stated that to get strong and grow, nothing beat compound moves and progressive overload; which I agreed with and understood even before discovering Starting Strength. Yet he put that type of split leg stuff and one-arm and single side barbell deadlifts in his perfect series and completely left off the fundamentals he himself claimed are so important. And the instruction he gives to breathe out when going down into the squat is pretty bad too.
The only person that impressed me on lunges are the old videos of Arnold working out performing barbell lunges walking around the gym. But how much did those really help him? Many of those guys had really bad form on their exercises, and did really questionable exercises back then.
Ahhh yes, there was once a time I used to spend my gym sessions doing silly bullshit too.
There was once a time I thought AthleanX was the holy grail of fitness advice (in fairness to him he does have some excellent injury rehab stuff)
But some exercises stick out in my mind as times when I started to realise how much gimmicky bullshit was on that channel
Skater squats, rocking triceps extensions and those uni lateral standing lat pulls all spring to mind