I buy and hold individual stocks for domestic stock market exposure, but I do not trade actively.
Since ETFs are just collections of individual stocks, I figured I might as well cut out the middleman. Whenever I have a decent chunk of money (about 3000$) that I want to allocate to domestic stocks, I buy a new stock from an industry which I am currently underweight. For example, last time I bought a wine company since I did not have any alcohol selling companies yet.
The drawbacks are:
(1) In the early accumulation phase, I am less diversified than with an ETF.
(2) It is slightly more work to go through stock lists and find out which one would be good to buy for improved diversification (you need to check which industries you are underweight and find companies from those industries.)
The benefits are:
(1) No management fee: even a TER of 0.2% adds up over time.
(2) Lower counterparty risk: ETFs engage in swap contracts or securities lending which induce some (small) counterparty risk. There is also the possibility of fraud by ETF employees. By holding the stocks directly, I avoid these risks.
(3) Less active trading than an ETF: since I buy and hold my stocks, I do not have such high turnover. ETFs sell whenever the index composition changes, incurring trading costs and - in some countries - creating taxable events.
(4) Additional small-cap exposure: I can also buy smaller companies which do not appear in the major domestic national index (and TERs on small-cap ETFs are about 1%!). Thus, I am also somewhat diversified on the size factor.
(5) Liquidity premiums: Some companies in Germany have two kinds of stock which are almost identical, just that one of them has voting rights and the other hasn't. When one of these is in the index and the other isn't, then the index version is much more liquid, and the other has much lower valuations. For example, when I bought BMW stock, I chose the non-index version which is 20% cheaper but grants the same right to dividends and company assets than the index version. It has a 1% spread, so it is not useful for trading, but for buy&hold the ability to choose the illiquid non-index stock boosts returns without additional risk.
(6) Better diversification amongst industries: domestic stock markets are often focused on certain industries, e.g. a large chunk of German stocks depend on the automobile and chemical industries. I can select my subset of stocks from index and non-index stocks such that my exposure to industries is more diversified than that of my domestic stock market as a whole.
For international exposure, I use ETFs to avoid the complications involved with withholding taxes on foreign stocks. It's just for domestic stocks that I do not see the great value of ETF investing.