You know what I hate? When people are unable to support or articulate any sort of judgement on something that isn't one of two extremes.
After trying the set for a few games out of sheer boredom, I have concluded that I personally do not think Merciless + Venoshock Toxapex is very viable. I will do my best to support this belief.
Your statement about the importance of BP is quite accurate; however I do not think Talonflame is a very fair example in this context. Brave Bird was not good on Talonflame simply due to its high BP. Rather, Brave Bird was good on Talonflame because it was a move that offered STAB fast priority from a very solid offensive typing that ALSO had high BP. Conversely, Toxapex's high BP Merciless + Venoshocks are tied to a typing that is quite poor offensively and come from a Pokemon with base 35 speed. Even with that being said, one must consider the fact that Toxapex is only firing off high BP moves when its opponent is poisoned.
The poison prerequisite alone makes Venoshock + Merciless Toxapex extremely unreliable. If your opponent has a poisoned Pokemon in front of a Toxapex in which Venoshock is revealed (or when Regenerator is clearly not revealed after Toxapex switches), they may simply switch into a new Pokemon and turn your high BP Venoshocks back into 65 BP moves coming off of a base 53 special attack stat.
For the sake of your argument, let us consider that you have been able to keep at least 1 layer of Toxic Spikes on the field and can now somewhat reliably hit high BP Venoshocks against non-Poison/Steel/Floating Pokemon. Is this really viable?
We have seen extremely strong wallbreakers with mediocre base speeds in the past. While a base 35 speed stat leads Toxapex to getting outsped by even defensive threats, the more crucial factor holding back Merciless + Venoshock's walbreaking potential is Poison's poor offensive capabilities. Consider the fact that many of the meta's most prevalent defensive types are Steel types. This is not similar to other offensive Pokemon walled by Steel types that can address this with coverage. Toxapex is just unable to touch Poison types at all due to their natural immunity to Toxic + Poison from everything except Salazzle. And even if you could poison them:
252+ SpA Toxapex Scald vs. 252 HP / 140+ SpD Celesteela on a critical hit: 99-117 (24.8 - 29.3%) -- guaranteed 5HKO after Leftovers recovery
Megagross and Tapu Lele are walled by steel types. Venoshock + Merciless Toxapex is completely shut down by steel types. If your opponent has a steel type Pokemon in their team and a Poisoned Pokemon out against your Venoshock + Merciless Toxapex, they can switch in their Steel type almost risk-free. Yes, Scald burns are effective, but they are also equally (if not more) effective on the defensive regenerator variant.
Furthermore, should you get the poison off, does this status not already severely cripple defensive Pokemon? As far as I can tell, Venoshock + Merciless is only strong against defensive Pokemon when they are not Steel or Poison and already crippled by a (Badly) Poison status. Regardless of how specific and narrow that situation is, the fact that these defensive Pokemon must already be crippled to lose to Toxapex makes its wallbreaking capabilities unnecessary.
So what about offensive threats? Well unlike a Talon Flame's Brave Bird, a Merciless Venoshock is coming off of a base 35 speed stat. While Toxapex's incredible natural bulk can allow it to tank hits from any non-Tapu, as readytolose states, the merciless + venoshock set does not seem to allow Merciless + Venoshock Toxapex to beat any offensive Pokemon (or frankly any Pokemon) that a defensive + regenerator Toxapex would not also beat.
Honestly, I'm not even sure Haze Toxapex loses to Clefable 1v1 but I think it's fair to say Merciless + Venoshock beats Clefable much more definitively.
Edit: Darklatias92 points out that this set can threaten poisoned Fairy types (such as the Tapus) on the switch-in whereas the defensive set cannot. That is a fair point. However, the fact that Merciless becomes immediately apparent after switching out and in just once (IMO) limits its ability to truly lure anything. It's also important to note that both Tapu Lele and Tapu Koko still beat Venoshock + Merciless Toxapex 1v1. Tapu Bulu can beat an offensive max HP Merciless Toxapex 1v1 if that Toxapex is not running any defense EVs.
Venoshock
might be run eventually as a tech but I seriously doubt Merciless will ever see usage that surpasses that of Regenerator's usage.
TL;DR: Merciless + Venoshock is unreliable due to the poison prerequisite. Similarly, the poison requirement makes Merciless + Venoshock's capabilities vs. defending Pokemon somewhat redundant. Furthemore, Merciless + Venoshock Toxapex is effectively incapable of threatening any relevant Steel type defensive threats beyond what a defensive Toxapex can, even with coverage. Merciless + Venoshock Toxapex is also unable to beat many, if any, relevant (offensive) Pokemon that its defensive variant can not also beat.
I'm interested in continuing this discussion with you or anyone if I'm missing something (which I honestly might be).