There are 2 very good reasons for building native integrations directly into your platform.
1. IP - If you build the integration you own it. This will be particularly important when factoring the valuation of your company and pitching to investors.
2. Self serviceability - Building a native integration into the most popular platforms will make it much easier for your customers to adopt your product. Being you are a startup and likely have limited resources my advice is to tackle the top 2 or 3 integrations your ideal customer is asking for.
That said, being you are in startup mode you likely do not have the capacity to build integrations into every platform your customers are requesting. Start by making your APIs consumable, even if only for your solution, if they are not already. Then consider either making the APIs available to your customers so they can build to their hearts content and/or use deal revenue to fund the build of a native integration (going back to point #1 and #2 above) whether that is done in-house or outsourced.