I have had at least half a dozen clients ask me this and build analysis for them around this specific topic in the last year alone. The answer largely depends on the circumstances (funding, time to market required, reliability of the platform provider etc). But it is a dilemma that many founders (particularly non-technical founders) face.

But in general I like being the master of your own destiny and keeping your tech stack fully in your control (that's not to say using open source tools isn't a useful way to still achieve that goal though.) I would say this: even if you are going to white label at the beginning, it is only a matter if when, not if, you will want to migrate in part or in whole away from this third party platform being the entirety of what you offer. In my experience these platforms typically offer too light or too expansive of a feature set and can be unreliable when it comes to things such as uptime, ticket responses etc. So generally I steer my clients away from it, or when necessary help them limit their exposure by creating a hybrid app that has elements you control merged with existing tools from the platform. the good news is that, in general terms, chatbots by and large are not tremendously complex (again, a few caveats aside) so building it with a software firm is certainly a plausible option to consider.

If you'd like to brainstorm or talk through specific parameters that could influence your plan one way or the other, or talk through how to roadmap potential issues that should be avoided (both contractually and feature-wise) feel free to reach out and we can schedule some time to dive in.