As implemented in the past, investors would either be recorded on the issuer's register or they would be in physical possession of bearer securities certificates.
Directly registering a stock acts as an artificial source of 'illiquidity' for investors who wish to precommit to a long term position, as shares held in a DHS take longer to sell, and are often batched at market prices (ie sellers have little control over their exit price).
These disadvantages have now been eliminated by the more modern and secure method of the electronic Direct Registration System (DRS) operated by stock transfer agents.
Settlement by physical delivery of certificates worked adequately until the 1960s, when a sharp increase in trading volumes overwhelmed the system.
The amount of paper that physically had to be moved around led to the famous "paperwork crisis" on Wall Street in the late 1960s.
Some internet communities, particularly subreddits involved in the so named GameStop short squeeze and subsequent wave of "meme investing", have advocated for the use of direct registration as a response to alleged fraudulent activity by brokers and hedge funds.
The use of DRS allows individual investors the status of direct shareholders of the issuer (rather than simply customers of a broker).