Why can't MX records point to an IP address?

I understand you should not point a MX record at an IP address directly, but should instead point it to an A record, which, in turns, points to the IP address of your mail server.

But, in principle, why is this required?

The whole idea behind the MX record is to specify a host or hosts which can accept mail for a domain. As specified in RFC 1035, the MX record contains a domain name. It must therefore point to a host which itself can be resolved in the DNS. An IP address could not be used as it would be interpreted as an unqualified domain name, which cannot be resolved.

The reasons for this in the 1980s, when the specs were originally written, are almost the same as the reasons for it today: A host may be connected to multiple networks and use multiple protocols.

Back in the 80s, it was not uncommon to have mail gateways which connected both to the (relatively new) Internet which used TCP/IP and to other legacy networks, which often used other protocols. Specifying MX in this way allowed for DNS records which could identify how to reach such a host on a network other than the Internet, such as Chaosnet. In practice, though, this almost never happened; virtually everyone re-engineered their networks to become part of the Internet instead.

Today, the situation is that a host may be reached by multiple protocols (IPv4 and IPv6) and by multiple IP addresses in each protocol. A single MX record can't possibly list more than one address, so the only option is to point to a host, where all of that host's addresses can then be looked up. (As a performance optimization, the DNS server will send along the address records for the host in the response additional section if it has authoritative records for them, saving a round trip.)

There is also the situation that arises when your mail exchangers are provided by a third party (e.g. Google Apps or Office 365). You point your MX records to their hostnames, but it may occur that the service provider needs to change the mail servers' IP addresses. Since you have pointed to a host, the service provider can do this transparently and you don't have to make any changes to your records.

DNS as a protocol has some different types of values, these are not interchangable.

It's important to note that DNS is a binary protocol with strict mappings between the type of record and the type of data that such a record holds.

For example:
An A record holds an IPv4 address (4 bytes of data, fixed length).
An AAAArecord holds an IPv6 address (16 bytes of data, fixed length).

An MX record, on the other hand, holds a name (a sequence of labels on the format <int number of bytes> <label> <int number of bytes> <label> <int 0>, variable length).

It's not possible for an MX record to have an IP address as its data.