Yes, a full range speaker, even if matched to the room and amp, can become the bottleneck, but it usually isn't.
I have been building speakers for 30 years and am a former industry member, so...
Most competently made speakers of a given size are going to work as they were intended, and the botteneck will occur elsewhere. Except in the following case:
The speaker has limited dynamic range for the kind of music and SPL you like. Many speakers which sound fine on jazz and rock at medium levels, fail to reproduce full range orchestral music, which can have almost 30 dB peaks.
Orchestral peaks sound hard or distorted, or the woofer does not reproduce the bass tones and pitch correctly (one note bass).
Even on jazz and rock, the increased dynamic capability increases the emotional content, imo.
This is why I stick to large, sealed box woofers (10 inches or more) and multiple midranges if needed.