You don't work hard to get avios, as I highly doubt avios are mentioned on your employment contract. Unless you managed to get your employer to agree for you to always fly BA, in which case you might have a reasonable expectation of earning avios for all your work travel.

If BA cancelled its FFP and voided all avios, I expect that you would still be flying the same amount for work, but getting nothing!

If you feel that you aren't being compensated enough for being away from your children, that's a matter between you and your employer...