In the case you described, the reboiler duty would be 3x normal duty at startup if you sized it this way. What is the impact on the reboiler operation after startup when you need only 1/3 the duty? What about at reduced column throughput? Will the reboiler still work at these conditions? If you put a 60% column turndown case on top of that, the reboiler will be very lightly loaded.
I'm assuming at the 3x duty case that you are starting up is with the column at full rates. Would you actually do this or would you start up at reduced rates and then increase feed as capacity is available?
There's another factor you may want to consider when setting the size of the reboiler design duty. If the feed/bottoms exchanger becomes fouled, what will the site do? Is the column shut down totally so the exchanger can be cleaned? Do you have multiple shells so you can take one out and clean the other at reduced heat transfer? Do you plan on just reducing rates in this configuration until the exchanger is cleaned and back in service.
All of these can be factors in setting the design duty. There isn't a straight forward answer but usually, I've seen minimal additional duty added to exchangers for start up conditions, definitely not adding in 200% additional area. Startup is usually handed by running at reduced rates. However, there is a cost associated with that and that may support adding in additional area.