Like I already said, I factored in a reasonable if not liberal cost (based on actual numbers) for insurance, maintenance, repairs (which by the way don't cost you anything if you don't actually need to do them), etc...
My van I've put about 40k on it in about 18 months (which is abnormally high for me, I had some longer trips in there, and a longer than average commute for most of it). It's a honda. If I wanted, I could probably get 300k out of it (it's about halfway there). But I'll probably keep it for about another 40 or so, and sell it running for about 3/4 of what I paid for it (somehow you never mentioned resale, mr accountant expert man). I don't buy anything if I don't expect to get at least 2 or 3 years and 40-50k miles out of it. Even if you drive it into the ground, you can get a few hundred bucks scrapping it.
But even with a new car, if you figure a $20k car should last 200k miles, you're essentially paying 10 cents a mile just to have the car. That brand new 2018 car is likely getting 30+ mpg. Gas prices (at least around the north east) are in the upper half of $2-3/gallon. So that's another 10 cents per mile. Oil change every 3k at $60 (if you go with the regular it's probably half that) is about 1/2 a cent per mile. Insurance if you don't crash into everything is maybe another 5 cents per mile. Average in another 5 cents a mile for repairs and other maintenance (ie $10k over the life of the car), and you're still at only 30 cents per mile of actual costs. Anything above that is just ERASING the costs. Which is to say that at around 60 cents a mile, you would be completely erasing the entire cost of a reasonably priced new car.
But a car is not really an "investment" in most cases, it's simply a cost (just like toilet paper is not an "investment"). So most people do not need or expect their personal car to pay for itself. So any amount that it does is gravy.
So the guy's actual costs for driving himself to the gig around $30 (assuming no tolls or other funny business). So that leaves $170 for actual gig pay. For 10 hours of playing, setting up, driving, etc... that yields about 17 bucks an hour. Or just taking into account 3 hours of performance time, $57 an hour. Maybe not great in terms of what's possible, but not horrible by any standards.
As far as the difference between reimbursement and deduction, just the nature of the entertainment business is that most or many things are under the table. Since this is a private party, I kind of doubt anything is going to be on the books. So it's really more like you're making $200 PLUS whatever your tax rate would be. In other words, if your tax rate is 20%, it's like making $250. Now, that's just hypothetical and you totally shouldn't do that *wink* but it shows another way of looking at the rate of pay and what's really worth and what the gig actually costs.
Now, if you feel it's absolutely necessary to get a hotel room (personally I would think nothing of just parking outside the party and racking out for 2 hours if I thought I needed to before driving home), then that blows your whole profit margin to hell, unless you're at least able to share it with someone else and find a pretty cheap one.
Besides that, most people for most gigs, don't even really factor in the cost of getting to and from. Most people would not think twice about driving 50 miles round trip for a gig. And probably not be counting their pennies of "oh, how much did my insurance cost for that, etc...?". So that cost of maybe $6 in gas and an hour of time is considered a given. So if you take that out of the OPs situation, you end up looking at closer to $20 an hour, so really the difference between this gig and a local one is about $3 an hour when it's all said and done. That's probably not a huge deal to most people. And for that local gig, you might still only get paid $100 or $150, and actually be making less per hour. If you consistently gig locally for 200 bucks, then that rate should have been added to during the negotiation process for the gig. So "our normal rate is $200 per person, we're going to need another $50 per person for travel for this one" (leaving room to negotiate down a bit if needed). In the end the negotiated price really depends on how "desperate" the band is for the work, and how much the client wants your specific band is willing to pay for that. In this case, the BL should have run the initial offer past the band for input before agreeing to a price.