That's not implied at all. The reason TPA is for practical purposes only observed under laser irradiation is because lasers are both high power (# of photons/time) and, under focusing, high fluence (# of photons/area, e.g.). This doesn't mean there is a zero probability of TPA under irradiation with an incandescent light bulb, but the lower temporal and spatial photon density, in addition to the fact that the TPA effect is nonlinear with the field strength, means that probability of TPA occurring in this situation is astronomically low probability.*

The point of my post being: many people erroneously understand "high intensity" to be synonymous with "high power". But in fact, in many practical applications of nonlinear (or even linear) optical effects, the fluence is an equally important, or maybe even more important, consideration. Therefore it's important to define what is meant by "intensity" - this will help to understand why many optical effects are not observed (note: not the same as "do not occur") under normal irradiation conditions. A laser can be a very high power coherent light source that is sufficient to drive many optical processes, but this alone may not be enough to stimulate higher order optical effects, even in molecules that are designed to have strong nonlinear optical response. This effect is taken advantage of in what is called a

Z-scan, where a nonlinear optical material is gradually brought into the focal plane of a laser (the z-direction) while keeping the laser power the same (see figure attached). This technique is one of the most common to measure the nonlinear absorptive properties of molecules in solution.

*For pedantic reasons, it's instructive to offer caveats to students about how the probability isn't mathematically zero, but on the flip side of the coin: to amateurs this can be counterproductive, and the opening post is a great example of why. It's hard to convey just how low probability some of these things are, and so it can be equally valuable to truthfully state that it basically just can't be observed in the timescale of human experience. I mean, you can rightfully point out that if you have a hydrogen atom just outside of the moon's orbit, there is a chance that its electron could potentially be found at the other end of the universe. The laws of quantum mechanics say so - the wavefunction never actually decays to zero, after all. But is that a useful thing to point out to someone who doesn't really understand the scales of probability involved?

(The figure I found by searching for z-scan on google. Reference:

Applegate et al. Optics Express 2013, 21, 29637-29642

https://doi.org/10.1364/OE.21.029637)