I have used the Salesforce service formerly known as ExactTarget to send emails to 6-figure lists. Other ET clients have included Microsoft, Apple, the Republican National Committee, etc. I've also used Marketo and Emma to send emails to 5-figure lists.
Mailchimp's pricing tool tells me that 200k subscribers will cost $875/month for up to 2.4 million emails sent. I will tell you that that is a fraction of the cost my employers have paid for the above platforms.
The thing to understand is that it is expensive to reliably send high volumes of email. Anyone can send high volumes of email if they don't care how many go into the spam folder. Sending spam is cheap. Sending email so that every single one gets to the inbox is expensive.
Why? Because to send high volumes of email reliably, you have to follow elaborate steps to prove that you're not sending spam. That means building lists through opt-in only, using clean IP addresses, warming up the IP addresses over time with progressively larger successful sends, aligning domain names across header fields and content links, applying every type of email authentication, hooking into common recipient feedback paths, monitoring and dealing with blacklist services, etc.
If you just want to slam a ton of emails out the door, and have some technical capability, you can save money using a "dumb" mail sending platform like Mailgun, Sendgrid, Amazon SES, etc. But you won't necessarily get "marketing" type features like link tracking, engagement reporting, responsive templates, etc. It does look like Sendgrid can give you a lot of that stuff for 200k contacts, for about half the cost of Mailchimp.