Agreed, I have worked hundreds of burglaries during my career and I would say with no reservation less than ten were what would be considered an home invasion.
Most of those were dope/stash houses getting hit by rivals.
I would also add that almost every one of those other residence burgs had no alarm services. One had the phone lines cut prior to the job.
Alarms work. In fact, local, state and federal goverment would be money ahead if they offered a tax rebate or break to offset the cost of service for homeowners.
Some insurance companies grant discounts on homeowner’s and motor vehicle policies for the presence of a sufficiently good alarm. That said, a silent alarm which does nothing more perceptible at the residence than turn on steady lights is most likely to get its cause discovered by the local gendarmes. Cell phone connectivity and battery back up is a must as you point out. Motor vehicle alarms, except those that quietly alert the driver when away, are virtually always overlooked as nuisances. (A rash of auto break-ins and thefts of radios happened a couple of decades ago at an apartment complex where I lived; I was away at the time but police reported that nobody bothered to report the repeatedly sounding alarms at what was likely a gang initiation).