TL;DR: You have no fucking clue what you're talking about.

If you're going to make the claim that you want common language to reflect accurate biology, why are you promoting the use of a paraphyletic grouping like fish at all?

EDIT To help visualize a paraphyletic group, lets imagine looking at a phylogenetic tree. It's confusing and difficult to effectively categorize organisms in the common grouping we know, like fish. To help with that, we're going to throw a piece of swiss cheese on it. In doing so, we cover up anything that we deem to be "not fish," while anything we can all agree to be a "Fish" falls within the holes.

"Fish" is a generalized term that has little scientific meaning. In it's broadest usage it includes any aquatic vertebrate that is not a tetrapod, which basically only excludes sea-squirts. Lancelets are commonly mistaken as fish, but they're not- they just look a lot like fish but they aren't really since they aren't craniate. Under your advisement, no one should refer to them as fish- and I almost agree with you.

Lampreys are also occasionally excluded from the paraphyletic grouping of fish. They're craniate, unlike the lancelets. However the lack of a jaw, fins, skeleton, and they're snake-like. For this reason, people often don't think of them as fish- even though they fall under the broadest definition of fish.

Stingrays are rarely interpreted as fish. They're craniate, have a jaw, but they have an odd body shape and a cartilagenous skeleton makes people unsure of their "Fishyness". Sharks on the other hand are commonly interpreted as fish, even though they're very closely related to Stingrays. Some people feel the need to separate sharks and fish though, since sharks have cartelagenous skeletons and fish have ossified bones. We call those fish Osteichthyes.

Eels are commonly distinguished from fish too! Unlike the shark they have an ossified skeleton, but they don't have the idealized body shape of a fish- much like a lamprey and, they don't have spines in their fins.

But what about Mastacembelidae fish? They're sold in pet stores as eels! So some people would say that they're not fish, they're eels. Those people would be wrong, they're not eels at all. They're in Actinopteryigii, and are more closely related to the idealized "Fish" than an eel would be, but their body shape alludes more to them being eels more so than anything else.

We've now shown that an entire taxonomic family is commonly excluded from the paraphyletic grouping of "Fish" and instead placed into the paraphyletic grouping of "Eels," even though there's no scientific basis for that.

We even occasionally mistakenly separate eels from fish within a family. Gobies are an excellent example of this. Within the family we have Gobiinae, or true Gobies. They look like fish. Anyone who sees them would say that. However we also have Amblyopinae which look a lot like eels, and are commonly referred to as such, even though they're definitively not eels.

I don't think I need to illustrate any further the contradictions on insisting on using paraphyletic groupings as being a preferable scientific alternative to unscientific common names.

You yourself made this exact same mistake. Orcas are whales, dolphins are whales. They're odontocetes, same as sperm whales. Honestly the only distinction paraphyletically speaking is their size- which is a fucking scientifically appaling way to classify any organism.