Are there any downsides to an Economy7 meter?

This is a rather unusual question, so I wonder who your utility is. Different types of meters and different types of billing are quite common. Letting the customer choose which type of meter is, to me, a little unusual. In most places I know of (US), the utility decides what meter to use. In fact, many electric utilities over the last 20 years have been gradually replacing meters with smart meters at no cost to the homeowner, but also with no choice by the homeowner. These smart meters provide many capabilities, including:

• Remote Shutoff - I haven't seen that myself, but others have reported on that in DIY SE. It makes a lot of sense from a safety perspective but also lets the utility shut you off remotely for non-payment.
• Remote Meter Reading - For a one-time cost to replace the meters, they save sending out meter readers every month. Eventually, that alone can pay for the meters.
• Detailed Usage Reading - A smart meter can report back every 15 minutes, or report once a day with 15-minute data for the entire day. Which, if done frequently enough, can lead to....
• Automatic Sensing of Power Outages - If the meters in a neighborhood stop reporting, the power is out. Send a truck. No need to wait for customer reports.
• Demand and/or Time-of-day Billing - This is your specific question, so more details below.

Historically, most electric utilities billed based on simple usage. Read the meter once a month. Subtract last month's reading from this month's reading. Multiply by the current price per kWh. Send a bill.

However, simple usage doesn't tell the whole story. It hides the true costs of generating power (peak plants cost more) and distribution (everything has to be sized for peak demand). There are two general solutions:

• Peak Demand Pricing - Figure out the peak demand (typically the top 30 minutes) for the month in kW. Multiple that by some $ amount. Send bill. This (a) compensates the utility for the hottest (or sometimes coldest) times when the overall system-wide demand is highest, resulting in the biggest peak plants are turned on and/or most expensive power is purchased from other utilities, and (b) encourages customers to lower their peak demand - e.g., by installing systems that can store power for use during peak times in various ways.
• Time of Day Pricing - This is similar to Peak Demand pricing, though a little simpler in some ways. Instead of a single peak for the month, the meter calculates total usage within a few (typically 3, but could be 2 or 4) different time ranges of each day or week. The highest rate is applied to weekday daytime (when businesses are open, air conditioners are running the most (in the summer), etc.) and lower rates to nights & weekends. This can have a larger effect, particularly on residential users (as opposed to commercial or industrial) who can't easily alter their peak demand but who can get in the habit of "do laundry at night", "run the dishwasher at night", "set back the thermostat during the day if nobody is home", etc.

Many utilities put in meters with these capabilities but don't actually charge accordingly, depending on local tariffs & regulations. But they generally have the capability with newer meters to do so. When they do start charging for peak demand or time-of-day usage, they don't necessarily give the customers any control over the billing method. So your situation of being able to choose the meter type seems odd. Hard to actually say, without a lot more detail about your utility and your usage patterns, whether a simple meter or a smart meter would be best for you.