You are making a mistake in booking your work travel on booking.com. Booking.com takes a cut out of the rate and therefore the hotel is not really interested in helping you.
The best way is to book directly with chain hotels. (Almost all the chain hotels guarantee that the rate they offer directly cannot be beaten by buying the same room elsewhere.) The advantages are, first, you get points that you can spend on your own leisure stays. Second, you get status points for each night. Third, if you already have status with the chain, this will be recognized, which it will not be if you buy from booking.com.
Once you have stayed ten nights or so, the chain will know that your business is of value to them, and therefore the hotel will, 99% of the time, put you in a good room.
So to answer your question, "how are the rooms allocated?": the hotel will know that a frequent customer is checking in later, therefore it is important to ensure that customer gets a good room. If the hotel has oversold the cheaper rooms, then our regular customer will be first in line to be upgraded to a better room, to make room for the booking.com customers.
(Yes; of course you should interact with the receptionist. If you are in Vegas, throw in a 40 USD "tip" will often get you a very nice upgrade. But I would not try that in Europe.)
I do most of my travel in IHG hotels (Crowne Plaza, Holiday Inn, Holiday Inn Express, Hotel Indigo). Through this, I have IHG Platinum status. I usually buy the cheapest room available with a double bed; yet I am upgraded to a junior suite or a club room with I guess 60% rate. Very rarely do I get put into a terrible room. If this happens I ask to see the manager, and if that doesn't work, I complain to IHG central customer care!
IHG has its pluses and minuses, like all chains, so you should research what kind of prices and, in particular, locations you are willing to tolerate. There is usually a shortage of the cheaper Holiday Inn properties in the centre of major cities, for example. Club Accor has a good chain with a very wide selection: you can always count on an Ibis being in the centre of town. Hilton would be my number two choice though for other reasons I will not get into.
If you will not meet the 60 nights per year or so required to be a "serious" customer, you can jump to a reasonable status grade by taking out the appropriate credit card. I know, for instance, that the current UK-issued IHG Visa card comes with IHG Platinum status for £99 per year, and comes with a 60,000 point welcome bonus (probably worth £300 if spent carefully). American Express Platinum (UK edition) comes with a number of high-status hotel cards as well, but the annual fee is an eye-watering £450/year. However, if you are really travelling around a lot, it might be worth the downpayment to make your business life a bit easier.
(This is not financial advice, you should investigate the options carefully before taking out any kind of credit card.)