Is there something specifically wrong with keeping the 8 precepts as a lay person? I know that the 5 precepts were intended for lay people. I know that in lay life, most people choose to only keep the 5 precepts, and there is no requirement to keep any more. I know that sometimes lay people take the 8 precepts temporarily. However, is there anything specifically wrong with a lay person keeping the 8 precepts on an ongoing basis? I know it's harder to do as a lay person as opposed to a novice(edit: I meant anagarika). But is it specifically discouraged or wrong for any reason?
No.

In fact, an anagarika (literally a homeless one) would observe the Eight Precepts on a full time basis, but in addition, would not maintain a lay household i.e. they would live a nomadic lifestyle or live in a monastery.

An anagarika is neither a novice monk (samanera) or a fully ordained monk (bhikkhu), but is a kind of informal state between lay life and novice monk, with far less rigid rules compared to monkhood. For e.g. they can deal with money and perform financial transactions. They can also cook their own meals. Monastic rules related to non-intimate interactions with the opposite sex also do not apply to them.

Usually, those who are interested in becoming monks would be asked to spend some time in a monastery, first as an anagarika, then some more time as a novice monk (who keep the Ten Precepts), before undergoing full ordination.

However, there are some people who have preferred to become full time anagarikas like Anagarika Munindra.

Even if one is not an anagarika, it is still foreseeable that a lay person could keep the Eight Precepts on a full time basis.