No. At least, not for Zerg. Banes are literally hatch-tech, and bane speed is lair tech, which generally comes at or a little after stim depending on the build. Strictly speaking, you don’t need to rush anything as Zerg against MMM, since ling-bane destroys MMM without any support necessary. Mines and tanks both are specifically needed because otherwise bio gets completely overwhelmed by Ling-Bane otherwise. It is, frankly, only when there is sufficient splash damage that Zerg players can’t overwhelm them that they need to get additional tech, and often still rely on Ling-Bane anyway.
I’ve had this conversation before, but Terran works very different from Protoss, who’s ground units are very specific but all of which synergize extremely well with each other.
This is NOT the case for Terran, who’s mech units in particular don’t synergise particularly well with bio for various reasons, though the primary two are friendly fire splash damage, and separate upgrades, but also tangentially, different playstyles. Terran tech is typically very generalised as a result, which is why they split into the two “core” compositions of “bio” and “mech”.
That doesn’t mean you don’t tech up though, as you’re often supplementing your army with widow mines/tanks, vikings, liberators, and of course ghosts.
Bio typically beats unupgraded Protoss ground, its true. Then charge and blink will actually beat stimmed bio without medivac support (and bio without stim, with medivac support), and chargelots in particular still remain very strong against bio - they’re the specific reason that bio goes into mines, and frankly almost never use tanks against protoss (as well as immortals and disruptors).
That said that’s generally because of the high health pool that chargelots have and their ability to gap-close easily. Obviously there are quite a few situations in which bio beats Chargelots as well, particularly when dealing with choke-points.
I mean, they do, it’s just not as common. That said, Storm is definitely not as strong as disruptors are, but they’re still a powerful and commonly used tool in TvP even at a pro-level.
Most of the strategy comes with builds, and frankly how tight a build actually is arguably matters most in TvX (with one or two BO exceptions such as Rogue’s Proxy hatch vs Creator in GSL).
What units you produce doesn’t change as far as core units go; but then again they don’t really change for protoss or Zerg either as it’s generally racially dependent. For Terran, it depends more on what your opponent’s composition is based around and what you’re trying to counter. Opponent is heavy stalkers or roaches/Hydras? You want tanks. Opponent is more Zealots or LingBane? You want Mines. Opponent is going into colossus? you want vikings etc. To some extent you can preempt this; particularly with Zerg as Tanks are okay against LingBane early on, and mines can be okay vs low numbers of roaches or hydras, but as those numbers start building you absolutely need to make sure you’re supplementing correctly.
You can argue that about any composition though; frankly for most people it comes down to more stuff beats less stuff, regardless of mechanics, as long as your macro is good, then you can make anything work. It’s why series like “Beating Grandmasters with stupid stuff” exists. It’s why challenges like “ghosts only” exist. Because, frankly if you’re good enough, anything can work against anything else. It’s really only when you start getting to the top echelons that that saying doesn’t hold true anymore.