Besides the issue of CNS penetration, there are several problems with that approach.
* A lot of the tolerance to GABAergic drugs is not caused by GABA-A desensitization but rather by compensatory changes in glutamate signaling. If you could get the synthetic Cl channel expressed in the brain then the same compensatory changes would still occur.
* GABA-A receptor signaling is complex. The receptors are not distributed uniformly but are enriched in certain places (the distribution differs by brain regions, cell types, and different parts of individual neurons). GABA-A channels with different subunit compositions have different properties, and those features are used to fine-tune signaling. Furthermore, most signaling is phasic, and the timing and rate of receptor activation plays an important part in signaling. These Cl channels lack any of that specificity. It is entirely possible that the overall effect would be to perturb brain function to a much greater extent then you normally see in sedative tolerance and dependence. In orther words, think of how muscimol is much more psychoactive than diazepam. These chloride channels would be even worse, because muscimol still increases Cl current using the existing framework of GABA-A signaling.
* Use of non-specific Cl channels could actually increase withdrawal and excitation. As an example, expressing the Cl channel in GABAergic interneurons would inhibit their firing, which would reduce GABAergic inhibition. That would be particularly bad for people using benzodiazepines because they are allosteric modulators and their effects depend on the presence of GABA. Although the Cl channels would also be expressed by downstream (excitatory) pyramidal neurons, GABAergic interneurons tend to have higher firing rates compared with pyramidal neurons and therefore are more susceptible to inhibition. Hence why local anesthetics tend to preferentially inhibit inhibitory neurons (this is why convulsions are a symptom of local anesthetic overdoses).
* Overdoses of those channels would probably cause fatal respiratory depression.