This has nothing to do with the TA or the compliance software (Concur, Traveldoo). Rather, it has to do with OP's employer who appears to have negotiated away the points and stay credit as part of whatever deal it has worked out with Hilton.
If you paid out of your own pocket, this would be easy to understand. You could theoretically offered a rate which earns and a cheaper rate which does not. You might choose the latter to save money. That is what your employer has done, likely through a larger travel wholesaler.
The place to start is to speak with your corporate TA and get the details (which it may not be authorized to share with you). If this is a HH error, you can get that fixed. If it is your employer's choice, you have a labor-management issue with your employer to discuss.
Traveldoo and Concur can book you in F and into suites at any property. But, they are able to restrict access to rates as well and that is their purpose.