I've generally had good luck with Booking.com and Trip.com in Asia and Europe. Expedia and Agoda less so. Airbnb can be useful in some cases, but more rarely these days. Skyscanner and Google are useful.
Pricing aside (you have to shop around and I agree you should check the hotel directly) some of the websites are better than others for showing you the area hotels are in (unfortunately you still have to go to Google or Apple maps with the address usually) . One of the things I spend some time on is looking at when flights arrive and leave and how I will get to and from the airport (free shuttle?) and wherever else I am going. Is there a metro line? An express bus into town? What hours does it run? If you've not got a tight budget and are just going to grab a taxi it doesn't matter as much, but even spendthrifts might gulp a bit at taking a taxi solo to NRT, IST or HKG from a far-flung hotel. And if you arrive too late you may get stuck with paying for an expensive room just to be able to travel the next morning when the border opens or whatever.
If you have a local (as in local to your country) deal finding website for flights they may be useful when airlines are practically giving a limited number of flights away. If you're flexible that can be a great way to reduce costs. Personally I have a spreadsheet of places to cross off and if a deal comes along that fits, I will try to grab it. I'm not sure subscription services are worth it, in my area the sites are ad-supported and therefore free to use.
All this is actually work, and takes significant time and effort that your assistant was doing (or not doing). On top of that, it's quite unlikely you'll get it perfect on the first trip to a new place. But you'll probably be close enough to roll with the punches and enjoy the trip.
Occasionally, you can get a routing or a price that's substantially cheaper by going through a 3rd party. I've used that and it's turned out well, but I won't for a $20 or $30 difference. For $200+ and a 3rd party I know, yes. Some of the dodgier sites have additional charges that eat away any difference anyway.
Depending on where you live, booking with a local website may give you additional consumer protections (such as free 24 hour cancellation of flights). On the other hand, sometimes you can book with the foreign website (of, say, an airline) and get a better price after currency conversion. That seems to be true with some flights to Central or South America.