I suspect that you are going to get a lot of apples and oranges, but what the heck....
I work in a very small division (4 people) in a pretty large company (110k employees worldwide). The company has a published travel policy document which documents the "rules".
In the case of my team, all of our flying is domestic US. We are required to pick a flight which is within $50 of the lowest priced flight departing within 2 hours +- from the desired flight time, using Egencia as our online travel agent. There are a ton of exceptions though - ULCCs like Spirit and Allegiant don't show up in the search results, I am allowed to not choose Frontier, usually based on the ridiculously long layovers I see. Policy exceptions have to be approved by my 1-over manager, but it has never been a problem as long as I am not trying to do something stupid. On paper, we have a preference for either Delta or American, but that preference doesn't necessarily override the price threshold. Also, Basic Economy fares are excluded from our search results, and Domestic First is always out of policy.
For rental cars, we have negotiated rates with National and Hertz and are required to choose them when they are available. The negotiated rates seem to be between $35-$39/day for most markets, so that winds up being a pretty good deal.
Hotels are a mixed bag. In some marketplaces we have negotiated rates with specific properties and are supposed to pick those first. If one is not available, we have a corporate preference for Hilton family first, IHG second. Each marketplace also has a maximum per night rate, so you wind up with something like "In Peoria, you should stay at the Radisson. Unless they have no availability. Then you should stay at a Hilton family property. Unless it is more than $120/night (base rate). Then you should pick an IHG property. Unless it, too is more than $120/night. In that case, just pick whatever dump you can find which is under $120/night". So I usually just pick whatever is closest to my customer site and my manager approves the exception.
Our policy explicitly states that any points/miles/freebies that we accrue are ours to keep, but we are obviously not allowed to choose more expensive options in order to maximize those benefits. For example, I can't pick a higher fare class, just to earn more points, or book a hotel room on a 5k bonus points rate.
All of our travel expenses are required to be paid on a corporate Citi card, so I lose out on the advantages of using my own affinity cards, but I find that having the bills paid automagically without me having to do more than go to a web page and categorize the charges to be a worthwhile trade-off for me.
It sounds kind of complicated when I spell it all out, but for the most part I am able to just select the most convenient flight, hotel, and car - and then go do my job. I'm not allowed to buy first, but I was upgraded on 80% of my flights last year.
Other than being away from home a lot, it's a pretty good gig.