Welcome to the forum, ‘petchyuk’.
I think you should consider yourself fortunate to have an insurer that has such an attitude towards towbars. I always declare mine when I arrange car insurance and by and large, there seems to be no increase in premium as a result.
However, I am aware that some car owners have fallen foul of difficulty arising from a failure to notify their insurer when making a claim for damage.
I haven’t actually towed anything since the early 1960s and when I finally hung up my spanners in 2003, I chose to purchase a new 6-berth motorhome rather than get involved with all the hassle of caravanning. I had 13 years enjoyment from my truck, spending time in France and Spain as well as visiting the Lake District and parts of northern Scotland among other jaunts.
Accordingly, all I need a towbar for these days is my cycle rack as I don’t consider it safe or sensible to carry bikes, particularly heavier electric ones, on the roof or attached to the tailgate of my Tucson. I specified one on ordering a new KIA Optima SW in 2016 which served me well and I had one fitted just after purchasing my Tucson in 2023.
As I was left high and dry in 1966 when ‘Irish-American’, my then insurer, went bust, I have ever since had a particularly cynical view of car insurers and nothing over the last 58 years has caused me to change my view of them. In a word, they are all 'shysters' and most of them are tax cheats with business addresses outside the UK.