It is clear from equations describing SBC that the bitrate of SBC doubles if you reduce the number of subbands by half.

Don't know anything about SBC, but that sounds very strange. Are you sure?

Yep.

Bit Rate (bit_rate) is calculated using the following equation:

bit_rate = 8 * frame_length* fs / nrof_subbands / nrof_blocks,

where fs, nrof_subbands and nrof_blocks denote sampling frequency, number of

subbands and number of blocks, respectively.

[https://www.bluetooth.org/DocMan/handlers/DownloadDoc.ashx?doc_id=303201, Sec 12.9]