What do you mean by "there's a net zero change in $\ce{H+}$ thus no buffering action took place"? The property of a buffer system IS to prevent drastic change in pH.
Buffer capacity, a measure of how much a buffer system can sustain a change in $\ce{[H+]}$ (aka. pH), (mostly) depends on two parameters -- the concentration of that buffer, and how close the desired pH is to its pKa. $\ce{H2CO3}$ has pKa's of 6.4 and 10.3. Given that the pH of blood is about 7.4 and better to stay that way, the base/acid pair, $\ce{[HCO3_^{-}]/[H2CO3]}$ (pKa=6.4) (plus a whole bunch of various proteins such as albumins in blood, all of which has its own pKa) does provide a good buffer capacity around that pH.
True, $\ce{CO2}$ is constantly removed through respiration, but it is also constantly generated by cellular respiration, making $\ce{H2CO3<=>CO2 + H2O}$ a "volatile equilibrium" and keeping both $\ce{HCO3_^{-}}$ and $\ce{H2CO3}$ in high enough concentration to sustain its buffer capacity.
HCl has a pKa of about -7 so it would make a good buffer around pH of -7. In an aqueous environment, all HCl molecules will 100% dissociate, and no $\ce{H+}$ will ever bind to $\ce{Cl-}$ because water itself will first "hijack" the proton as $\ce{H3O+}$ (pKa=-1.74) before $\ce{Cl-}$ by about five order of magnitude.
---EDIT---
You may be thinking that when cells release $\ce{CO2}$ to the blood, $\ce{H2CO3}$ would be the first product, and in order for $\ce{H2CO3}$'s conjugate base to work as a base to absorb any extra $\ce{H+}$, first it must release a $\ce{H+}$, resulting in no net change in free $\ce{H+}$ and hence no capacity in balancing extra or insufficient $\ce{H+}$ to maintain the pH. Indeed, if $\ce{H2CO3}$ is the ONLY chemical species in the blood when it would not be a buffer. A buffer requires at least two species -- a potential proton donor and a potential proton acceptor, both of which in high and comparable concentration. pH is a measure of external free $\ce{H+}$, a result of final proton balance of all the acid and base in the blood, dictated by the Henderson–Hasselbalch equation. Thus when $\ce{H2CO3}$ is released in the blood, the blood's basic pH will causes most of $\ce{H2CO3}$ to become $\ce{HCO3_^{-}}$, releasing free proton. Again IF that's all the $\ce{HCO3_^{-}}$ in the blood after being made from $\ce{H2CO3}$, the blood's pH will drop, but there is already abundant amount of $\ce{HCO3_^{-}}$ in the blood, helping the system to reach new equilibrium. Of course, the buffer capacity of blood is not infinite. If there is so much metabolic acid being produced that it shifts the ratio of $\ce{[HCO3_^{-}]/[H2CO3]}$ toward excessive acid, acidosis would occur.