I have never heard of a child who is 100% self-motivated to do the practice 😁, at least not on string instruments as it's such a tedious job. DD has been playing for nearly 6 years now and while playing pieces has always been fun, scales and technical exercises are a different story. We are very fortunate as her teacher writes very detailed technical tasks in DD's practice diary so I can always point out to the notes and it's not just me being a nagging parent, but some other figure of authority telling her what to do. I still need to remind her to do structured practice and focus on difficult bars.
In DD's case predictable daily routine helps too - she knows that she comes from school, has a snack, some downtime reading/playing, then practice time so her days are very structured and she's happy with that.
Lots of multi-instrumentalists do early morning practice, before going to school - our violin teacher's DC practises 6-7am, and they're 7yo. Mornings are often more productive - sadly no one in our family is a morning person so never worked for us 😞
I've never offered any "bribes" but many people do and it seems to be working, too.
If anything, I find practice harder not easier moving up the grades. DD did grade 4 with barely 40 minutes of unstructured practice and not even every day, now at grade 8+ it's impossible to get away without working on the tricky bits separately - and this is just basic technical stuff, musicality, interpretation and expression aside. I guess it takes general psychological and physiological maturity, not just years of experience playing the instrument - though some children appear much more mature and focussed for their age than others. Also, it's probably slightly easier for girls at younger ages - we know exceptionally talented boys who didn't make enough progress for the amount of talent they have, simply because they struggled with practice due to a relative physiological immaturity. I think there is no universal recipe for practice, a lot will depend on the child and their individual music journey.
On an easier instrument though DD (11) is completely independent in her practice at the same grade 8 level - I don't even know what's going on as she practises at school and I can only see the results in concerts. It's only strings and piano that are hard work 😁