Most of insurer's assets are already liquid, not just short-dated assets, e.g. 30-year treasuries. One investment theme I've always thought was good for insurers is to monetize some of that liquidity in the form of long-dated illiquid investments with high credit quality such as infrastructure projects. Another favorite of mine is ECA loans that are typically government backed, but the backing is tied to a specific counterparty so they are illiquid.
If you ask an insurance risk officer how much liquidity is in their asset portfolio, they'll respond, "A lot!" But before you can think about monetizing liquidity through these types of illiquid investments, you need strong liquidity risk management to be able to quantify exactly how much liquidity you really have over a range of scenarios.
Unfortunately, the easy solution most institutional investors go for in these low interest rate environments is the search for yield by going down the credit spectrum. That rarely ends well.