With the exception of those representatives new to the business and actively building their client list, agents will likely have a full roster of clients (writers) that demands much of their time. There are contracts to negotiate, edits to suggest, manuscripts to submit, bills to pay, etc. Add all that up and you get this: Agents are busy people, and aren't exactly racing around the world looking for a whole bunch of new clients to sign.
That's why writers should be wary of any agent that seems overly enthusiastic. Real agents don't offer you representation with a snail mail letter, complimenting generic aspects of your work. And here's a big tip: Real agents don't advertise. They get too many poor submissions as it is, so why would they spend money to attract more? If you see a Google Ad for a literary agency, such as the infamously bad New York Literary Agency (a member of the "20 Worst Agencies"), that agency is a scam. They will lure you in and then mention money.
Sure, real agents are still looking for new writers. As one rep put it, "We're always searching for an unpolished gem." But remember: If something seems too good to be true, it very well may be, so make sure you're in reputable hands before signing anything.