Each time lingering wrist pain made Mark Teixeira unavailable last year, the Yankees’ failure to protect themselves with a legitimate backup was underscored.

Kelly Johnson filled in inelegantly and Brian McCann and Chase Headley reluctantly. Garrett Jones, this year’s initial Plan B, was better, but mostly in comparison to what was around in 2014 as opposed to a desirable option.

Which has made Greg Bird’s arrival and emergence such a positive. The Yankees can more comfortably allow their leader in homers and RBIs to heal from a deep bone bruise near his shin because Bird has performed so instantly comfortable at first base and at the plate.

However, that Teixeira has not been available at all accentuates a problem the Yankees are coping with now, but which every team deals with over the course of a long season — playing shorthanded.

The conundrum is when a valuable player (such as Teixeira) has an injury that will keep him out for multiple days, but the organization does not believe 15 days. So the team does not want to DL the player and lose him for two-plus weeks, when perhaps he only needs 5-7 days to heal sufficiently.

Teixeira was unavailable to the Yanks for the third straight game Thursday night. GM Brian Cashman said the anticipation was Teixeira, who fouled a ball off his shin Monday night, would not be able to play for seven days, though there was encouragement about how the switch-hitter was moving around that perhaps that could be cut by a day or two.

Still, it is ridiculous a team should have to play shorthanded. I have long been a proponent that — at the least — a team should have a three-to-five-man taxi squad available to them and declare which 25 players are active for a game in the way players are deactivated for games in the NHL, NBA and NFL.

If not that, there should be a DL that is shorter than 15 games. Fifteen is just an arbitrary number. Why not 10 or eight?

If there were a seven-day DL, the Yankees would have put Teixeira on that list and called an extra player up for a week.

At a time when the whole sport is looking into ways to lessen injuries, playing shorthanded promotes injuries. As Joe Girardi noted by not having Teixeira available, it made it more difficult or impossible to rest other players or to remove them from blowout games to provide a breather.

MLB’s chief legal officer, Dan Halem, said changing the DL rules has come up at previous collective bargaining negotiations and he anticipates it will again when talks with the players begin in earnest, probably around next spring training (the CBA expires after the 2016 season).

There has been some budging in recent years in this area. There was a seven-game concussion DL created (Bryan Mitchell is on it right now). Also teams can replace players who leave the team temporarily for bereavement or birth of a child. This would just be an offshoot of those — an ability to temporarily replaced a player hurt, but not hurt enough to be gone for 15 days.

However, Halem said clubs worry that teams will use phantom DL stints to manipulate the roster when, say, they want to skip a starter or use someone else. Cleveland GM Chris Antonetti said he is against changing the DL rules because of the nefarious potentials, particularly for richer teams to exploit the system by being more willing to have expensive options at Triple-A or having little concerns for travel costs.

But that could be mitigated in a bunch of ways.

The main worry with the manipulation involves pitching, namely starting pitching. So make it that you can just use, say, a seven-day DL for position players. At present all DL stints come with documentation from the club to the Commissoner’s Office signed by a team doctor. So MLB could just be more of a clearinghouse with its medical people to make sure injuries are legit. For example, Teixeira had an MRI that showed a significant bone bruise. It is easily documented.

Or you could have a system in which a team could only use a seven-game DL stint three times in a year, so there would be a risk in using it for fake reasons and not having it at a club’s disposal for a real case.

It just seems that when the sport can avoid teams playing shorthanded it should. Because it improves the competition and limits exhausted/injured players from having to be on the field because someone else is hurt or keeps the hurt player from feeling he has to rush back so his team is not shorthanded.