As ever with science/policy there is what is known to be true scientifically, and what is pragmatic policy making which balances costs and benefits.
Legally you would be perfectly in the right to go out and about.
Morally... it's less clear.
The positive LFD suggests there is a high chance you are still infectious. And it is certainly well within the realms of possibility that you could still be infectious, because we know it's possible, if more unusual. If personal experience helps, in everyone I know the LFD got gradually lighter and within 7-10 days was completely clear.
Look at it this way - there are rare cases of people still shedding virus after months, but it would be silly to make everyone with Covid isolate for months, just in case. That would have a massive negative impact on their mental health, fitness, disruption, economy etc, and people would just end up ignoring the rules. So the public health specialists and government had to come up with a rule that would be the best of both rules - isolating long enough to keep the majority of infected people out of circulation, accepting that it won't be long enough in all cases, and some people will be out spreading virus. But across the whole population, the rule should reduce spread enough to help keep the numbers down. That individual though could infect a lot of people potentially.
For someone who can work from home and not take a financial hit, I would say that morally you should stay home and wait for a clear test.
If you're going off to see vulnerable people, again, it would be best to stay home and wait for a clear test.
If you need to go to the office perhaps you could ask to wfh until clear.
If you're going to have to take a big financial hit from staying home longer then it's a much more difficult decision. Legally you'd be doing nothing wrong. Maybe you could minimise the risks as far as practical - going for a walk when it's quiet, wearing a decent mask, avoid people.