I can't get your link to work, but is this the same article you've looked at: http://www.twowheelblogs.com/intensity-factor-and-training-stress-score
I think part of the confusion is that yes, blood lactate levels roughly match a power^4 (closer to p^3.9 as RDO mentioned) curve but 'Stress' is not being strictly defined as blood lactate level.
In terms of NP calculations the p^4 averaging is actually closer to a RMS style A^2 averaging commonly used to analyze the average amplitude of a sinusoid but the resultant NP is not a p^4th term, the averaging is performed at the 4th power then the 4th root is used to take it back to a linear effective power term. I'm sure you know this, but the blood lactate vs. power exponent is related to this pseudo-RMS averaging and not to the definition of 'Stress'.
TSS as defined in the article above is:
TSS = exercise duration x average power x an intensity-dependent weighting factor
But yes, once you normalize it to a rider's FTP (not necessary as mentioned in the linked article but helps generalize the metric) you end up with: duration*IF^2 represented as a percentage of FTP for an hour. Some of that is just mathamatic gymnastics but the key is that TSS is not defined as a literal mapping of blood lactate level but as duration*power*intensity_weighting and it turns out that the intensity weighting is basically IF and 'power' when normalized to a rider's FTP is also IF.
From a practical standpoint a lot of folks already feel TSS overvalues short bursty efforts in that it's possible to 'inflate' TSS values by doing some very hard bursty work then padding the workout with a lot of easy time on the bike. If TSS was proportional to IF^4 that would be much more pronounced and I doubt many folks would consider that a more accurate estimate of overall stress.
I think the bigger mathematical problem with TSS is that TSS is not piecewise linear in summation as you've pointed out. Break a ride in half and in general the sum of the TSS for each half does not equal the TSS for the entire ride. That may be valid in the sense that the sustained ride offers less recovery time then two separated rides so it's possible the sustained ride actually has more stress but it's a very hard thing to prove. But the bigger problem is that CTL and ATL as long and short term daily average TSS rely on linear summations or actually averaging which implies piecewise linear summation of the individual ride TSS values. That's a bit of a head scratcher as it's hard to take a linear (or exponential as is used in WKO+) average of data values that can not be summed in a piecewise fashion and at one point Andy was talking about a TSS v2 but I haven't seen anything about that in a long time.
FWIW, you're not alone in your NP/TSS skepticism and there are plenty of outspoken coaches who dismiss the concept and prefer to track things like kj of work performed which is completely linear with average power and duration. I guess the question is whether you find NP, TSS, and from it CTL valuable in terms of guiding your training and predicting fatigue and or freshness. If so, use it, if not then there are plenty of other methods.
I do think it would be interesting to choose alternative input channels for the PMC in WKO+. IOW if you could select kj of work or say TRIMPS for folks tracking HR data or even miles or hours as the input to the PMC you'd still get a visualization of Bannister's impulse response model but could see which workload tracking metric better tracked your fatigue and freshness. IMO, the real beauty of the PMC is seeing how long term and short term average workloads trend and how they relate to each other and not strongly tied to what workload metric you prefer.
-Dave
