Is it objectively a bad thing if the entire multiplayer experience in a fighting game boils down to "who can true combo first"?
For reference, "true combo" isn't frequently used as a term for traditional fighters, as practically speaking, every combo is a true combo of sorts if your opponent (or game) lacks a burst/combo breaker option. The term is (more or less) exclusive to platform fighters. I only mention this to add context behind its usage.
As for the question, I wouldn't necessarily say this is a problem for the genre, even for a game that you may think is like that upon first glance.
Taking Marvel 3 as an example, the game is incredibly volatile - even top Marvel players drop combos all of the time in that game due to a combination of a high mental stack while playing, high execution required, as well as potentially unoptimal conditions, such as low meter or improper screen placement (i.e corner only combos). Add in Marvel 3's less-than-stellar netcode, and this all is a recipe for hectic and unpredictable matches.
Street Fighter 2 is known for high damage combos, but it also has the best fireballs in the history of the series, as well as a strict timing window to special or super cancel. Shown below, most characters have about a 4-5 frame window to cancel from a normal to special. They often have one extra frame to cancel into a Super Combo, but even so, these are not very lenient windows. Hit stun is also shorter in ST. So although damage is high, the common combo is often just two moves.
All of this is to say (type? You know what I mean): yes, it might be a bad thing if the only aspect of a fighter that matters is getting the first clean hit against your opponent. But in reality, I don't think this is the case for the vast majority of fighting games on offer.
