I own CEFs along with everything else (funds, stocks, etfs, etns, etc).
CEFs have some very useful qualities which make them worth owning despite the higher ER. Your typical CEF will have an ER around 2%, half of that to pay for the leverage.
The benefits are: (1) a safe and cost effective way to use leverage, (2) a way to access obscure/illiquid investments, and (3) easy money/withdrawal management.
Most CEFs invest in fixed income assets (about 2/3 of them). Those that invest in equities tend to focus on utilities, mlps, and reits.
Now is a good time to buy CEFs as the discounts have widened due to (IMHO) irrational fears of inflation.
For someone new to investing in CEFs I would suggest starting with an ETF of CEFs like VanEck Vectors CEF Municipal Income ETF. Ticker is XMPT. Its an ETF made up of 70 municipal bond CEFs, and it tries to rebalance itself so that you invest the most in whichever ones have the biggest discount at the time.
https://www.vaneck.com/etf/income/xmpt/overview/
Once you get comfortable enough to invest in individual CEFs, I'd recommend buying John Hancock Tax-Advantaged Dividend Income CEF (ticker HTD), provided it has a descent discount. Its a CEF that is 50/50 utility stocks and preferred stocks. All of the dividends are qualified, and they pay a fixed amount monthly. I like them because they do a very good job at keeping a positive UNII, while growing the dividend and NAV over time. The current yield is 7.55%, but on a leverage adjusted basis it is only 5.18%, which they can maintain easily given the assets they are invested in.
Comparing HTD to Wellessley Income and the S&P 500. The 10-year total return on Wellessley Income is 6.87%, the 10-year return (on NAV) for HTD is 10.57%, finally the 10-year total return on the Vanguard S&P 500 index (VFINX) is 8.76%. The 10-year trailing Sharpe ratio on HTD is .69, for Wellessley it is 1.04, and for VFINX it is .65.
HTD
P.S. My CEF investments are in a taxable account. So I limit myself to tax advantaged options.