BTC supply, transaction fees and security of the network

One of the most valuable aspects about BTC as a monetary asset is its scarcity, limited supply and low inflation. This makes BTC an excellent candidate for a store of value, i.e. digital gold. With that in mind, we know that over time the inflation rate of BTC would decline ever more, i.e. block rewards would decline until no further BTC are left to be mined. After that, the only monetary incentive for miners to secure the network would be the transaction fees. If the future of BTC is one of digital gold / store of value then it would be reasonable to expect that investors would be buying and holding long term, i.e. they would not be transacting. Given that transaction fees would be the only financial incentive for miners at some point in time would the "store of value" future of BTC not pose a threat to the security of the network? How would this apparent conflict be resolved?