If it is used in the right contexts it's fine, I think a lot of things have come up where it's used incorrectly or not right for that context.
So BAME lumps together dozens of ethnicities, nationalities, and experiences as if they are one group. For example, 'BAME underachievement' is overall improving, but hide that some groups (e.g. Black Caribbean boys) are still disproportionately excluded - in this context breaking down in subgroups is more appropriate.
Also grouping so many groups together, can ignore specific forms of discrimination or specific differences in discrimination experienced by particular groups.
For example, BAME people face disparities in health outcomes is true, but it hides how and why those disparities differ between Black and South Asian patients as an example. Or even Black women compared to Black men.
But BAME can be a practical umbrella term when used well. It’s fine if it’s clearly defined and followed by disaggregated data - breaking down smaller subgroups (e.g South Asian, and then Indian etc).
So for something like, summarising large-scale data (e.g. NHS patient diversity, ONS reports) where there are small sample sizes for individual groups, BAME can be a practical umbrella term.
Also before BAME became common, ethnic disparities were often ignored or underreported. The term forced public bodies to acknowledge that outcomes differ by race and ethnic groups in policing, health, housing, and education.
Also, when used with sensitivity and clarity about the benefits and limitations that ‘BAME’ is imperfect and may not reflect individual identities, but it’s used here for consistency with national reporting standards.
BAME is also short, recognisable, and easily understood by the general public and policymakers. In communications like press releases, policy briefs etc it can be useful shorthand to talk about policies for ethnic groups without a long list of lots of different ethnicities.
In short, the type of communication and context mamatters. I was trying to make a brief point on a mumsnet thread, if i was having a longer, in-depth conversation about racism in education etc, a brief I would use the specific ethnic groups related to stats etc.
Some organisations or advocacy groups may use BAME as a collective identity in solidarity, or other terms like global majority or just the specific ethnic group are better.