Yes, broadlog and tracking logs are huge tables, and the query could last some seconds, but 10 minutes seems abnormal, because email fields are indexed. For comparison, it takes about 1 minute for me for 14 millions of contacts and broadlogs/trackinglogs purge after 1year and half.
I tried with limiting the result set of the 2 query activities to 100 lines or not limiting at all, the same response time. (the matter of this limitation treshold would be to reduce RAM memory dedicated to XML context, but in that use case, only one recipient so the volume is quite small).
One optimization may be: find first the recipient.id corresponding to the email entered in the form field, then search the trackinglogs and broadlogs by using the recipient.id.