The biggest problem with Kaspersky is the biggest problem with anything from Russia. You need to trust Russians and as someone that has had business dealings over there, that trust is incredibly misplaced. Russia is largely a gangster run land of lawlessness where everything is for sale for the right influence or highest bidder, and where most people will use whatever they have over someone against someone. The most common business model in Russia is not 'Customer first or Customer always right' but rather 'As a customer you should be thanking us for providing this, we owe you nothing.'. 10 years of business dealings over there and this is almost always how it is..
As such, I find it incredibly misplaced to trust something as intimate as an antivirus product coming from such a place. As much as I love some of their software I have found it incredibly unwise to install anything 'Russian' on any of my most important assets. I have a cut story where we started to use Yandex Browser, and within 3 weeks all of my sons gaming accounts became compromised or attempted to be compromised. Steam, Origin, etc. Once Yandex was exorcised from our systems and passwords were changed the problems resolved. I'm not a believer of random coincidences with that much correlating data. Especially since every one of the compromised accounts was traced back to mother Russia.
So regardless of how good their stuff can be (and it can be really good). You should consider if that trust is misplaced with your most sensitive things. Regardless of how untrusting people are of US corporations, almost everyone trusts Russian ones far less.