Your synthesis is alright
but there's something I'd like to add -
thank you for your confirmation as well as another possibilty. I thought about it, and I think my way is faster
That's correct, alkylmagnesium grignard are more reactive than arylmagnesium.
..because the alternate method has Ph-MgBR, and Ph is a ring which is much bigger than CH3, so for that to attack the nucleophile, it would take longer time because of steric hindrance!
Alkylmagnesium grignard are more reactive for a different reason than steric hindrance of arylmagnesium grignard though.
Of Mg atom and the Ph group, Mg is more electropositive. Now you put 'delta charges' for the alkyl-metal bond and see what becomes 'positive' and which one 'negative', in order that we see how the probable mechanism works.
Let's do the same for the carbonyl group C=O of the ketone. Put the partial positive and negative charges correctly.
Does the Ph-Mg bond seem likely to break in order that Ph becomes an electrophile to attack the nucleophilic centre of carbonyl group
OR does it seem more probable that the
more electropositive Mg might somewhat coordinate bond to the more electronegative of C and O in C=O?
To answer now why arylmagnesium are less reactive - because the aryl group is more stable than alkyl - does aromatic stabilisation sound plausible? Delocalisation of the charge you're going to put on the Ph group in the grignard?