It wouldn’t be accurate to say “you can’t”, but Microsoft doesn’t make it easy.
Whether you’re moving mailboxes or PST data to Office 365, your imports are throttled; that is, Microsoft imposes a limit on how fast you can move information into their data centers. The exact speed of your import process will vary according to a variety of factors, including what protocol (IMAP4, MAPI, or EWS) you’re using, what migration tool you’re using, and how many concurrent threads it can spin up, how busy the data center you’re importing into is, and the mix of item sizes in the mailboxes or PSTs you’re importing.
The problem with this throttling is that it’s largely opaque. Although Microsoft publishes “observed data,” my own observations have shown that migration throughput can vary widely based on these factors and a bunch of others besides, possibly including the phase of the moon and whether you have recently said anything disparaging about Microsoft anywhere on the Internet.
Recently I had a customer who wanted to migrate 30TB of PST data to Exchange Online Personal Archives. While this might sound ridiculous, it makes perfect sense given that Office 365 E4 plans include an unlimited-size Personal Archive for each mailbox. That’s a hard deal to beat… if you can figure out how to get the data in. At one point, in a fit of frustration we asked Microsoft whether we could just send them a bunch of disk drives containing the PSTs. “Of course not,” they said (with “silly boy” being the unspoken coda to that phrase). But it turns out that Azure is now providing bulk import of data by sending disks to them: the Windows Azure Import/Export Service is now in preview. With any luck, we’ll see a similar service from Office 365 in the not-too-distant future. And when it happens, remember, Andy Tanenbaum had the idea first.