You can, but you've a little higher chance of getting a false negative. It's all about probabilities. I'll do my best to explain, but be aware I don't know what the probabilities of incorrect test results actually are, so the numbers in this are just for illustration.
A test can give you the wrong result in two different ways: a false negative means the test says you don't have it but you actually do, while a false positive means the test says you have it but you actually don't.
My understanding is that the LFTs are slightly more likely to give false negatives and PCRs slightly more likely to give false positives. So, plugging in some numbers to illustrate this, let's say if you're actually infected and you take an LFT, you've got a 1% chance of the test being negative. If you're infected and you take a PCR, you've got a 0.5% chance of the test being negative.
Now, if you're a member of the population with no symptoms, your chance of having Covid at any given moment is (about) the Covid rate, i.e. the proportion of people in the population who do have Covid. Not sure what that is right now, let's say 1%.
If you do have symptoms, you have a higher chance of having Covid, let's say 50%. Again, this is made up to illustrate!
Here's the thing. If we test everyone without symptoms with a LFT then we'd expect a false negative in 1% of 1% of the total people we test (as about 1% are positive and 1% of them will get a false negative). That's 2 in 20,000, which isn't too bad. If we test people with symptoms with a LFT, 1% of 50% will get a false negative. That's 100 in 20,000, quite a bit more common.
If we test people without symptoms with a PCR, 0.5% of 1% will have a false negative, so 1 in 20,000. Test those with symptoms and it's 0.5% of 50%, so 50 in 20,000.
So, using my figures, which I can't emphasise enough are just made up ones to illustrate how it works, out of every 20,000 people without symptoms, we'd have 1 less false negative if we used PCR compared to LFT. Out of every 20,000 people with symptoms, we'd have 50 less false negatives if we test with PCR compared to LFT.
So, given that PCR tests are more expensive, and more of a faff to do than LFTs, it makes sense to use them primarily with the group that's more likely to be infected, as we'll miss fewer cases that way.