Yes, BMW sell a reasonable number of base models.

I agree with the plan to order one configured exactly as you like it. If dealers in the OP's area only have loaded up models, that is because they have found that there are sufficient purchasers without the patience to wait for one, who are thus willing to buy off the lot. Might as well sell those purchasers all the options, especially since those options have a higher profit margin than the base vehicle.

I factory-ordered my last four BMWs, and the one before that was traded with another dealer to get the colour and options I wanted, while allowing me to purchase from my local (servicing) dealer.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue