BMX style 20" Wheel bike ?
https://www.raleighusa.com/mxr20
there are other companies .. too 'making' just BMX bikes
the bicycle motocross rider does not sit down and pedal, but stands.. , so your boy really wont outgrow it..
but may want a different style of bike.. depending on what their friends are into
Most-all are rebadged for each importer , by a big multi brand OEM factory to cut costs.*.
And so at same price ...more same than different ..
* you did mention costs ..
Who you buy from may matter more than the brand, (In independent bike dealers) so pick the Shop First ..
....