It depends on the job really. Some jobs nowadays the clients prefer non-button cameras due to the angle you can get.
The primary problem with something like a bluetooth is battery power. It's great for what, an hour? Then what?
Your typical new home is going to be over an hour and if you lose part of the video, even 10 minutes, you probably aren't getting paid and the client will reject the shop. In addition, you often do multiple shops per day and can often have many within 10-15 minute of eachother. Not nearly enough time to recharge the entire battery. (You can always buy more cameras, but at this point you could have gotten one button camera).
Some clients wont allow cell phone recorded videos period. Others prefer them due to the style of interactions.
Sometimes a head mounted camera is needed because of higher counter tops and you need to follow the money.
Generally speaking though, the vast majority of jobs are suitable by a button camera, so you get your best bang for your buck with that. Here's a spreadsheet of video shopping companies and the links to sign up. It also tells you (for the companies who responded) which cameras and devices they allow for their shops.
[
docs.google.com]
CEO The Mystery Shoppers Depot
US Wide route shopper with 12k+ shops completed over 48 states and 6 countries.
Airbnb host based in Chicago and 10% discount if you mention this forum