For election officials, you don't want a representative sample, you want a maximally diverse sample. If a certain party has e.g. 40% support and you randomly draw 6 election workers per polling place, the chance of giving them 50% or more on any polling place is quite high. Include some adjacent parties and you'll get some very one-sided groups.

Of course, you can't do a lottery and then demand the chosen self-identify which party they support, nor can you trust them to be honest. The result is that you can only have people who volunteer.

I think the system we have in Slovenia is quite close to optimal: every party who got at least X % in the last election gets to submit applicants and each polling place gets 6 people, who have to have been referred by different parties, with priority based on the rank of the party in the last election.