I think the reason people object to exempting buses and taxis while imposing it on many cars is not a failure to understand that the ULEZ is only part of the strategy, but that nothing seems to be being done about buses. I agree that the TfL can deal with bus emissions, but they are not. Most TfL buses emit visible clouds of soot when accelerating, they idle in traffic jams (and the nature of the routes mean that they often idle for long periods in jams in the worst pollution hotspots), they idle at bus stops (which are often sited very close to schools and areas with high pedestrian traffic, so as to serve those areas), and they are not consistently Euro VI vehicles.
What people object to is the fact that TfL's response to vehicles they do not pay for is to impose taxes verging on fines (an overnight visit, at £25, is half the level of some fixed penalties for dangerous offences at £50, and for a 5 day a week commute is £62.50, more than the fine for driving a dangerous vehicle), and their response to anything where they pay the bill is to try and get a few more years out of outdated, polluting vehicles, with a 100% exemption. The New Routemaster, which was being built up to 2017, is a Euro V engined bus and more polluting than the vehicle it replaced. This is the main bus used in the highly polluted central area.