I have booked through Travelocity many times (Delta flights) and have found them to be very good. I had to cancel our BVI trip due to COVID and I was very pleased with their customer service. I was able to chat with a real person and got all my credits applied without hassle and when it came time to re-book they redirected me to Delta who had all our information on file. Not a fan of kayak or Expedia. All that said I did book with Delta direct for my next trip.
I have not found that any of the old tricks (clearing cookies, using booking sites, using a different computer etc) has made any difference in the last few years. So without any obvious benefit of using a booking site, I will stick to booking with the carrier from now on.
I finally booked two weeks ago and now I could have saved $900 if I waited until this week (thank you Kayak for the very incorrect price prediction!). It's all a crap shoot right now.