we had lots of trouble with them many years ago (NEF). Fail to eject, cartridge jammed in chamber, action jumps open when fired, hinge knuckle loosening/breaking etc. They were of poor quality back then. I don't know if improvements were made after that time. I would try a late model, just to see. Some guys say they have no problems, so perhaps they have been improved. They certain are handy.
The one I liked best was an H&R with full wood stock in 30-30. But, it too needed to have a new hinge knuckle. I had a Smith make one instead of replacing it with factory parts.
The new ones (H & R) still have extraction problems, the chambers tend to be rough and poorly finished leading to the extraction problems, especially in smaller calibers like .223.
I have an NEF rifle in .17 HMR . Most accurate rifle I own ! When it was new , it had failure to extract at times, extractor spring sticking . after 200 rounds it is broken in and i have no other issues .
The 17's are very accurate... on a day with a 10 mile side wind my son broke 37 eggs in a row @ 150 m with a Sportster in 17 HMR.
How many have you personally examined? IMO this is a "squeaky wheel" situation... a relative few bad eggs that get reviewed online and then the opinions get regurgitated, ad nauseum... IME there are relatively few problems with H&R firearms... it is a simple, solid design and prone to fewer problems than actions with more moving parts. The chambers and bores that I have scoped are actually quite good, with fine tooling marks and little chatter. The basic extraction system of all break action single and double rifles is far more effective with rimmed cartridges, but works well with non-rimmed cartridges given certain parameters are in place; namely, clean brass, properly sized brass, loads that are within SAAMI tolerances, and properly cleaned chambers... some of these are not issues in other action types with a more manifestly positive extraction... but when dealing with the break action rifle chambered in a non-rimmed cartridge this is something that "should" be expected... and if a problem does arise it is easily remedied... the nice thing about Handi's is the ease with which they can be worked on... Google any firearm model from any firearm brand and you will find detractors and issues, even with firearms costing many thousands of dollars.
So if the implication of your post is that I'm making this up and posting BS, you are very wrong. Will every one have the problem? Of course not. In fact what I have noticed is that most of the problems are with the smaller chambers.