Ha! That's a great idea - add it in as a billable item on client invoices.
In other words it is commonly expected that professionals come equipped with the tools of trade. Not that this is set in stone, but that's the state of affairs and trying to do it differently is an uphill battle.
Not always. Construction firms hire a lot of what they need for each job, because it is not economical for them to store and maintain the enormous variety of tools/machines that they need over the course of a year. They'd need a huge warehouse and a whole team of people to manage and maintain all the equipment, and at that point you may as well start running a hire company.
They don't invoice you for each rental fee in an itemised fashion, for the same reason they dont invoice you for each screw, each nail, the fuel for their vehicles etc: you don't give a shit.
Actually, it's not the parts that are peculiar, it's the amounts and configurations that tend to vary. In any case, it makes good economic sense for everyone involved to handle labor and kit separately.
Sometimes heavy equipment is added on by contractors. For instance, I can dig this ditch with a shovel, or we can rent a backhoe, and have it done in a few hours.