The battens seem sturdy now but they would sag in time
Its a bit more complex than that and dare I say it scientific. The minimum size was revised in 1997 but its not just that the battens may sag there are various other issues.
A wider batten will enable greater pull out resistance for the nails aiding wind lift resistance.
Battens these days are supposed to be graded but many are not, I believe. If a battens meets the BS's it effectively guarantees their lifespan.
They provided rigidity to the roof structure though more of an issue with trussed roofs.
They provide adequate safety of the roofers during the work.
Furthermore, your roof tile warranty with the manufacturer will be worthless if the tiles are not fitted in accordance with the manufacturers specifications.
In addition to the above if you suffer from any wind damage in the future and the insurance assessor is on the ball it would be reasonable for any home insurance claim to dismissed for the same reasons.
You might want to check the gauge adheres too.
I dare say there are a few other reasons too.
I would not accept them.
The roofer is just being a cheapskate at worst or ignorant at best.