Many placed I have worked in past, software quality is often talked about but in reality it is always compromised mainly for cost and time reason. The usual explanation is that since the turnaround time to fix the bugs are not that high, there is no need to spend more time on testing. Market research has shown that organization, who invests heavily in testing procedure and tools, reduces cost long term since they are not constantly going backwards and fixing things over and over again.
Even in an organization where this is a QA team, often quality starts and finishes with them, I feel quality is responsibility of the entire team, which includes management and BAs, and of course developers. Try looking at your development cost and chances are that 60% of the development resource is spent on identifying and fixing defects. By not introducing defects in the system and implementing proper tools and procedure to identify them earlier on, development cost can be reduced and eventually increases team productivity.
Quality should be enforced right from the beginning of the project (yes even in requirement gathering phase), project leader should focus more on quality rather than quick delivery.
To conclude this blog, there are various level of quality required for software, some mission critical software needs to have close to 0% defect, where as some software can handle more. Quality is an ongoing process, which should be built in to the SDLC, quality should not be looked as burden and requires commitment right from the top level management. Any testing tool can identify the defect but only the ones which falls under the testing criteria, most software are so complex (at least the ones I have worked with) that there is no way you can test the complete software, in this scenario implementing good quality business process (along with testing tool) is the way to go.