The top concern with Klaviyo is they send email using Sendgrid. This means they are one step removed from the inbox. Deliverability really matters today and Sendgrid have a very poor sender reputation, especially when sharing IP pools with other senders. So your reputation can be mixed with that of other senders, some of them bad actors.
The second concern is the level of effort to get working. Unless your client is willing to accept long implementation times, Klaviyo is not out of the box and requires a lot of manual email coding. Clients will push back against this in terms of time and cost. You can easily show how flows like welcome series and RFM are out of the box, see the BigCommerce video on the site as an example.
The third concern is cost. For 10k contacts, Klaviyo charge 175/mo. For some that means more than the cost of the Shopify platform. Use our dynamic pricing tool on the home page for more.
And don't forget support. Klaviyo do not provide any phone support. Feel free to use our phone/support details on your website for the best white-glove treatment.
PS When a client is switching from Klaviyo and other platforms all flows and templates will be converted for free by our team.