The small number of people who determine these options retain most of the political power. All methods of collective decision-making involve ambiguities and spoiler effects. All methods are vulnerable to manipulation and strategy. The sole exception is a majority vote between two non-negotiable options, like a vote on whether to end a meeting. When there is a large number of choices, many problems emerge when everyone tries to choose at exactly the same time.
Voters have to choose without knowing how everyone else is going to vote.
It's also more difficult for candidates to run targeted campaigns, and for voters to find the candidates they prefer, if they can't operate at their own pace. A common solution to this has been the two-round runoff election, where a few leading candidates are chosen from a large pool in a primary election, and a final winner is chosen in a second election. Direct Representation can be seen as an extension of this idea, because it effectively uses a continuous runoff election to choose new legislators. Voters can make a new pledge at any time if they feel that their second-choice candidate is making more impressive progress toward membership in the legislature than their favorite. A candidate can win a seat at any time, given enough pledges.