There is another way to deal with the situation, and that is to work for yourself.
My own Mouser/Farnell/Digikey/Microchip/Golledge/RS annual spend is well into 6 figures. If my assembler calls up and the P&P machine has thrown a tantrum and is short of a part, I buy it while they're still on the phone and have it shipped. Sometimes I have sufficient stock at hand, in which case I jump in the car and have it with them within 90 minutes. Paperwork? What paperwork? The accountants are a long way from running this asylum, thank you.
Regarding TI, many of their development boards and eval kits are so cheap now that I don't have any problem in spending $20 on something that they're clearly not making a dime on, merely covering their costs.
It is very rare I get samples, maybe once or twice per annum, and these are always for parts that just aren't available from the usual distributors, perhaps needing an NDA signed also.