You can set your rates however you want, but I think your rate is too low and incorrectly calculated. Your "standing there doing nothing" cost is
(expenses + profit) * hours - you must pay the rent 24/7, and for heat and electricity during your daily hours of operation.
If you were to hire an additional person you wouldn't be paying rent for an empty building if you each work eight hours per day consecutively. With two people, having one of you come in four hours early and the other stay four hours late lets you stay open sixteen hours each day and have two of you available half of the time.
Chatting on the phone for free doesn't boost your profits as much as doing complicated work that pays a premium; expenses are partially fixed with variable additions for consumables and wear on expensive machinery, profit can be increased by doing difficult work that other shops can't do.
Back to your "shop rate", the difficulty (skill level, and any specialty equipment) of the work should be factored into the rate. If you could stand on the side of the road with a tape measure and earn $45 / hour why invest hundreds of thousands of dollars to earn the same amount?
You could hire a helper and offer 'basic work' done by them for $45 / hour (or less), if they are going to want $20-25 an hour the remainder is what you earn to have them use your equipment (and take up space). That tends to show that you might want to charge more for your time and extra for expensive machinery that makes doing the work in a reasonable amount of time possible.
Your second paragraph is the crux of your problem:
"Now let's imagine we take on a job that's going to take both of us 2 days (~12 billable hours each) to complete working together at the same time.".
The number of days is the days you must pay rent:
if you worked on the job for one hour per day and took a week off you would need to be able to pay for a month's time with $45 * 24 = $1080.
if one of you came in for 12 hours and then the other came in for 12 hours the job would be done in one day; that's $25,920 per month, calculated the same way as before.
So don't miscalculate your expenses and rates.
If one of you can do the work in 24 hours or two of you could do it in half the time (which is actually seldom the case) then either way you charge
rate * people * hours.
The rate could vary by the skill level of the person (and thus their hourly wage) and the cost of the machinery amortized over it's lifetime.
It makes a huge difference if one person is working on a job or it takes twenty people, you are not going to be able to pay for twenty people by charging $45 / hour.
Also twenty people aren't automatically twenty times faster. If you send one or two people to the hardware store to pickup a couple of hundred dollars worth of lumber is it going to be ten or twenty times faster, cost you ten or twenty times less, to send ten or twenty people instead of two.
There an optimally efficient number of people for each task, some tasks only need two people some of the time; there's a joke about needing a few people to screw in a lightbulb.
If it's particularly high up it might take two to carry the ladder and one to hold it - if it's a one person job then you can't charge for two, if it takes two people you must charge more (and long ladders are more expensive than short ones).
You could offer a small discount for additional people working simultaneously on the same project, that's not unheard of, but additional people for free simply leads to fewer billable hours. It's only if you bid a fixed price and had a due date to meet where you'd want to assign additional persons to the project, but that's a different pricing model than what your question asks.