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Warning: this may be an extremely naive question (if so, please enlighten me).
Many applications of relays require a flyback diode to protect against inductive voltage. I'm unable to find any relay that incorporates a flyback diode.
Since it's such a common need, why don't relays include a flyback diode inside the relay package? Are there just too many factors to consider, making it hard to guess the circuit's need?
There is simple answer to this question - there are many flyback schematics and the reverse diode is the simplest one. Although it has one big disadvantage - it makes the relay to switch off very slow.
This way, sometimes other schematics are to be used. There are several examples:
simulate this circuit – Schematic created using CircuitLab
There are quite a few relays (also contactors/breakers) which are powered from AC. Putting a diode inside renders them useless for AC applications: -
There are several types of relay that are of the latching type and these also require a reversal of voltage - a diode would render this type of relay useless in that application: -
See also this answer for high speed switching of a relay.
There are actually are (or were) a few which have had internal coil suppression. For example this Teleldyne one. They've not been very successful commercially in the general market. Maybe in the automotive market.
It probably has more to do with stuff like history and second-sourcing than anything technical, though I fail to see much advantage in putting a diode internally. It forces a polarity on the pinout and results in a sub-optimal electrical life for all users, for a very small saving.
There's no PCB generally inside a relay so it would have to be welded or crimped or soldered into place.
There are relays that include a fly-back diode, but percentage wise, not very many.
If you go to this Digi-Key page which lists signal relays (less than 2 amps) and scroll to the right, you will see under the column Features that one of the attributes you can pick are Diodes.
Here, only a little over 5% of the relays listed incorporate a diode. For power relays, the number with diodes is a little over 3% of the total.
So they do exist. But why so few? Obviously, it keeps the cost of the relay down, even if the user has to add their own diode. This also lets the user select a diode that exactly meets their needs. And it is cheaper (and easier) for a user to add a diode to a PCB (which is an automated process) than the manufacturer add it across a relay coil (which may have to be manually done).
There is also a reliability problem. Most relays are sealed or, at least, not made to be disassembled by the user. If an internal diode fails, the relay becomes useless. Since the diode cost is much less than the value of the relay, it makes more sense to add the diode externally.
