Hi @Anonymous, and welcome to Power BI! 🙂
It's a tricky subject to quantify, and I don't think that there's a truly objective answer to this. I would hope that your implementation partner has a good reason for their trepidation around custom visual usage rather than just seeing them as generally bad - they're missing out if so!
I'll offer my perspective as someone who produces visuals, and had been using custom visuals in the production of BI assets for some time before I started doing it myself. This area of the forum is not as busy as the others, so it'd be good to hear if anyone else has some perspective to share around this.
With any requirement, you'd need to evaluate on a case by case basis for the data you're intending to use it with. As a rule of thumb, if you have a use case for a particular custom visual and if it performs well for the data you're putting into it in your report, it's going to perform pretty much the same if pinned to a dashboard.
Regarding visuals in the marketplace, they can be published by anyone - they undergo a degree of testing by MS when being published to ensure that there's nothing obviously wrong with it, but QA is typically completely on the producer and their response to and resolution of any issues raised by users.
It is typically in their best interest to produce these to as high a standard as possible to ensure continued usage and adoption. In my experience I very rarely have issues with any I've used, and I've been fortunate that bugs have been minimal for the ones I've produced. That being said, some due diligence should be observed with anything you're producing for consumption by end users - for example, if your data model is not optimally designed, it'll perform poorly irrespective of whether you use core or custom visuals. There are a lot of moving parts to a BI solution.
Visuals that are marked as certified in the marketplace have undergone further testing by the custom visuals team to ensure that they meet their standards. This is not to say that if a visual is uncertified, then it should be avoided - there are a number of reasons why people may not choose to go through the certification process and there's a good few visuals that I use regularly that aren't certified. Your mileage will vary, depending on what your objectives are.
Not sure if this is wholly constructive to answering your question, just my two cents. Happy to discuss further if you want to follow-up.
Good luck in your Power BI journey!