Hi, assuming that cutadapt trimmed off the first 20 bases of your froward and reverse reads, then you're right. Note that primer sequences in the reads can interfere with both merging and chimera removal. Make sure that you correctly removed the primer sequences.
Losing a large fraction of your reads may not necessarily be a bad thing. Check this comment by Dr. Benjamin Callahan. You can run a rarefaction analysis to find out if the resulting sequences are enough for the downstream analysis for most of your samples. If that's the case, then you're fine.
The lost of large fraction of reads is more likely caused by the data than the DADA2 pipeline. To verify that, you can download some similar data with mock, denoise the sequence with the QIIME2 version you're using and see what you get. If the mock looks as it should be, then it's not the DADA2's problem.
As mentioned above, a positive control helps you to find out if there's something wrong with the bioinformatics. You can test your ideas with the mock sample if you happened to include one in your sequencing run. If not, you may want to go ahead with both approaches and judge the results with your knowledge about your samples. Use the one that makes sense to you.
-Yanxian