A conference needs to proceed in a timely manner. The conflict of interest are needed to select reviewers. If a reviewer is asked to review (at a top conference they might have already agreed to review N papers at this time) and finds a conflict of interest, the reviewer will inform the chair of the program committee and the paper needs to be reassigned to another reviewer. What is easy for a small conference with less than one hundred submissions becomes an administrative nightmare with more than a thousand submissions.
Even with a small conference, there is no time to go out and start recruiting reviewers after submissions. That is why there are program committees, which might or not might give discretion to assigned reviewers to assign to sub-reviewers (in their research group) or recruit other sub-reviewers outside. Usually, shortly after the submission deadline, reviewers are invited to bid on papers (in which they declare their confidence in being able to do a good job at reviewing for a particular paper). Papers with a conflict of interest are usually already excluded for a particular reviewer from bidding. During this phase, reviewers can also state conflicts of interest. After the bidding phase (usually a few days), a typically automatic assignment of papers to reviewers is made, giving reviewers a relatively short time window to prepare the reviews. For conferences with a very large number of submissions, this process needs to be modified. Instead of bidding on papers, the conference might choose a different mechanism, such as assigning papers and reviewers to sub-topics.
Not declaring conflicts of interests interferes with this process. It is not the task of the conference organizers to do the conflict of interest declaration. Automatic tools are actually dangerous. People publish under different names, change affiliations, and there are even people with the same or similar names in the same field. The current process has enough informal safe-guards to deal with difficulties arising from the difficulties of identifying conflicts of interests.
There is also a concern in the community about various forms of manipulations. There have been cases of groups of scientists helping each other to get published by manipulating the peer review process. Openly declaring conflicts of interests is our duty as submitters in a peer-reviewed conference.