Never used the service but that's a bit weird not to have emails. Did you ask about if they actually send emails or not? Would be interesting to know if it was just being blocked or there was a problem sending them. Maybe other customers of Forge can comment.
My personal (bad) experience with Forge service
I have signed up on Laravel Forge since March 2016. I am not the guy that I click on wrong buttons especially when it comes to signup and pay for a service. Although I am just one guy, and I am pretty sure I clicked the individual package ($10), Laravel Forge signed me up on the team package ($20). How can this possible done? My mistake? I never do such mistakes. Anyway, lets assume I did that mistake (once in my life). Where is the welcome message (email) that says I have signed up for Laravel Forge in Team package for $20. Guess. There is no such email. No welcome mail - nothing. Not even a single email every month that your service is being renewed and $20 will be changed in your card. No billing emails of course. Everything hidden. After 3 months I realized that I have been charged for $20 instead of $10. I contacted the support team and without any further explanations or questions they told me to downgrade on my account and they will refund me the extra money (3 months x 10$). It was too easy, you know like its a regular thing (people contacting about their wrong subscription). At the end, they have only refunded the 2 months ($20) instead of 3 months ($30) and of course I canceled my subscription.
I don't have anything against the service or the people running it. Its my responsibility to double check everything. It was my bad I had blind trust due to the "laravel.com" domain but I was wrong.
My advice to all people signing up to the service, to double check what they are charged for and my advice to people running Forge include those emails like welcome to the service, you have sign up for a paid service for X$ at X Package etc and every month you charge their card to send an email. Technically is easy, I hope decision is not that hard :)
[EDIT] I forgot to say that I am also LaraCast subscriber and I receive every month a receipt email about the $9 being charged in my card. That's the proper way :)
I too think the only reasonable way is to email customers every time you charge them. Companies like DigitalOcean, Apple and Microsoft does so.
Not sure if it's legal requirement too.
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