Before starting Semaphore, our company was an agency. One of the biggest reasons we were bored with agency work is that, since we worked with startups and 99% of them fail, we'd always build only the v1 of everything. No experience of what's it like when things lift off.
The technical challenges of a growing product far exceed what we could experience as an agency. If something is outsourced it's almost by definition either not very challenging or not very successful yet.
If a product goes the distance the scale and stacks will change significantly.
You've mentioned "Being closer to the product owners" — in practice what makes an even greater impact is being close to product users. That gives a deeper sense of meaning to the work. (If not then you're definitely not for a product company. ;)
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