Without further knowledge of at least what else is on the character sheet of the character that is making the "Ignore Fire Immunity" attack WE absolutely cannot say that.
The player with a specific character sheet might be able to, so what, that happens in any number of contexts for any number of available attack options.
But we, at a design level, absolutely cannot.
If you are operating under a sufficiently restrictive class system, not something the OP limited itself to bringing in other sources of options creature types and item modifiers, then you might be in a position to come close to saying that at a design level about a specific class. But even if you want to obsess over D&D we can't really say that for certain since we aren't restricted to purely class based abilities.
We CAN very thoroughly build a very narrow edge case of a specific character. Of a pure fire specialist after all selectable options, with no other options other than fire damage, and add Ignore fire immunity to that.
But lets take a moment to note... that if that pure fire specialist genuinely has no other options except fire damage... fire damage is STILL their best option against fire immune targets (even if it does nothing) because, it's a tautology, we had to literally design them to have no other options. Their only option is always their best option by definition bypass or not.
Lets also point out in the moment they have any other attack options this changes. And it doesn't matter whether you are uncertain about other possible immunity or not. Not knowing if the target has lightning immunity as well does not stop your lightning attack from potentially being better, especially if your character is actually just flat out better at lightning attacks, and especially if their is also a known or unknown vulnerability to lightning on your target. And it was deaddm, not me, who brought in "Spectacular" vulnerabilities by damage type as the first and foremost reason to have damage types at all no less. Just because you have a fire attack with ignore fire immunity on a character does not mean you don't have other typed attacks which are flat out better on your sheet, better because of a vulnerability on the target (known or unknown), or better because of other contexts. Because banning Ignore Fire Immunity from game design for being naughty isn't just about the hyper specialists, it effects all your potential characters/classes/options.
Now that edge case of the fire wizard with literally no other option, yes, it's been in the argument since the OP. Technically only by implication, but close enough. And like I have said since the OP. You can give them bypass fire immunity, or not. Because all it will do is either let them use their good option in one more type of encounter match up OR will result in just another no good option encounter match up. Neither of those things is in itself a problem at all, or a design level solvable problem if it were. Both these outcomes will happen in other contexts anyway. Mechanics that result in good and bad contextual match ups are only tools made available to the players that then fall completely out of our hands as designers.
The thing we should worry about with specialists is only if their specialty allows them to get SO good that allowing them to experience "good match up" is itself a disaster. The fire specialist being too good with ignore fire immunity only happens if the fire specialist is ALSO too good when the match up doesn't include targets with Fire Immunity at all. The ability to simply apply damage like you otherwise would isn't and pretty much cannot be in itself the source of that problem.
On the flip side while it's bad to "no good option" a character too much of the time, we cannot actually fix that by only "carefully" giving fire immunity to exactly 10 out of 107 monsters in our monster manual. Nor can we fix that OR hurt that by giving out a fire immunity bypass at an appearance rate in game that we also cannot control.