Definitely encourage the use of controls, I think they are a must.
So in a typical random genomic DNA experiment where there should be generally even coverage of the genome through random sampling, low levels of contamination would not be expected to cause any significant issues with consensus sequence generation.
However, in amplicon sequencing the situation is notably different because you can very often get the situation with particular samples that fail to amplify some tiles at all (e.g. in the case of a low copy number viral genome, or a primer-binding site mismatch) but other samples generate high coverage of the corresponding tile. That’s a potentially majorly confounding situation for consensus generation as all of your reads could be coming from other samples in that region. It could end up looking like some strange recombination in downstream phylogenetic analysis if that tile contains a variant.
I wrote more of an explainer here, which you might find helpful:
https://artic.network/quick-guide-to-tiling-amplicon-sequencing-bioinformatics.html