For the Premier League it is the gift that keeps on taking. The seasonal problem of exactly what to do with Uefa’s second string, the dreaded Europa League, is something Arsenal must now face up to as their final Champions League fixtures approach. There is already a creeping, slightly doom-laden orthodoxy here. Albeit one that could prove paradoxically self-destructive in the longer term.

Arsenal must win against Dinamo Zagreb at the Emirates on Tuesday night, hope Olympiakos are simultaneously beaten in Munich and then win by two goals in Greece on 9 December to reach the knockout stage elite come the spring. But is there any point in actually trying?

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Finish third in the group after semi-heroic last-ditch failure in Greece and Arsenal will find themselves playing in Europe’s secondary vase for the first time since 2000. This is the most likely outcome for a team who, despite some recent setbacks, must still consider themselves in with a chance of winning the Premier League. Chuck in a new year resumption in Europe and that chance recedes even further.

The Europa “round of 32” kicks off on 18 February. For Arsenal this raises the prospect of a trip to some bruisingly motivated European hinterland before three league games in a week that includes trips to Manchester United and Tottenham. Struggle through that and the spring run-in, source so often of a season-saving run of form, could feature as many as nine additional midweek fixtures, plus the added dislocation of a Sunday afternoon league programme.

All in pursuit of a trophy that seems to have a deleterious effect on English teams generally. Last season Tottenham played 10 Europa League matches and dropped 14 points in subsequent Premier League fixtures (seven more at the end of May would have given them fourth spot). Everton dropped 16 points after Europa League ties. This season Liverpool have dropped nine. The sense of a wider Europa virus is present elsewhere too: of the Premier League’s six Europa representatives in the last three years, three have changed manager before the start of the following season.

“We want to take it seriously,” Per Mertesacker insisted this week, of the endgame to a Champions League campaign that has brought three defeats in four games so far. Still, though, there is a creeping conviction, a whisper at the fringes that Arsenal would be better off somehow contriving in plain sight – a draw and a loss would do it – to shunt Zagreb up into third place in Group F, in the process earning themselves “a Blighty one” back to the mainland.

And yet, for all its persuasive gloom, this is to look only at the narrowest picture. The fact is, there are many more reasons, including obvious self-interest, for Arsenal not just to enter the Europa League gladly, but to take it very seriously. The first is perhaps the most important; fans like winning trophies. There has been a tendency to overlook the tangible achievement of back-to-back FA Cup wins, as though only the billionaire-hogged “major” trophies count. For those who support rather than distantly critique their team there is nothing like winning a cup. And Arsenal would have a middling chance of winning the Europa, while they have (sorry) no chance of winning the Champions League.

Beyond this there are broader domestic concerns. Apologies again. But, yes, we need to talk about the coefficient. The notion that the Europa League would be harmful to Arsenal overlooks the fact that ignoring the Europa League could be much worse. The maths here is very simple. England are now three points above Italy in Uefa’s ranking table, hauled in by a six point swing last season. The Premier League’s best recent season, 2011-12, when they were four points clear of Serie A, will disappear next year. Italy lead on the three seasons following that. The upshot of which is that either England crosses its fingers and hopes Juventus’s success last year was a blip. Or somebody, somewhere does something in either Uefa competition to still the very real danger of losing that fourth Champions League spot. Who would this still-distant disaster harm most on recent form? Arsenal.

This is the real motivation not only for getting into the Europa, but for taking it seriously should it come. Arsenal have finished fourth six times in 10 years and never higher than third in that period. Spurs have finished fifth five times in the same period. It is self-evident both are best placed to do themselves, and each other, a favour here. A win, or even a semi-final would make both clubs’ hypothetical Champions League future a lot more secure. Each victory counts in the points table. Winning the Europa is worth up to 13 points more than going out in the last 16; or in other words an extended sinecure on that fourth place.

This is no small matter. A great deal of money, prestige and sustained interest is invested in that fourth-place jackpot. Should Arsenal slip into the Europa, as seems likely, they would be among the stronger teams (with all due, head-scratching disclaimers) in the competition. Given Arsène Wenger’s sense of enlightened commercial self-interest, to undervalue it now would be hugely counterproductive. Not to mention a most untimely betrayal of the domestic league in its moment of need.

And this really is the best argument for rolling up the sleeves and having a proper slog at Uefa’s most tin-pot tin pot. English football has a miserable recent history here. In the Uefa Cup’s first 13 seasons English football provided five winners and two beaten finalists, from Spurs v Wolverhampton Wanderers to the thrills of Spurs v Anderlecht, Graeme Roberts and all that, in 1984. After which: not so much. The Heysel ban bit hard. Sixteen years passed before England’s next winner, Liverpool in 2001. In 14 seasons since the Premier League has provided just Middlesborough and Fulham as beaten finalists, plus the largely forgotten bonus riches of Chelsea’s victory in 2013, without which the coefficient battle really would be in full retreat,

At the end of which the final headcount makes for salutary reading for anyone with half an eye on the decline of the English national team and the lack of European depth in the Premier League generally. Since Tony Parks’s save won the Uefa Cup for Spurs 31 years ago only 21 Englishmen have played in a Uefa Cup or Europa League final. Of the last 36 semi-final slots just three have been filled by Premier League clubs. Does the Premier League really deserve that Arsenal-tinged fourth spot? It would be an amusing coincidence if the current single-minded pursuit of Champions League football (and cash) led to that path being abruptly narrowed by the failure to achieve more broadly.

In reality, turning on the light for a moment, it seems almost impossible Arsenal could choose any other path than trying to finish as high as possible in Group F. But there is a much greater incentive here than simply keeping up appearances. If it comes, entry into the second-string should be celebrated rather than grudgingly borne. The Europa League deserves our belated respect. If only for the very obvious reason that taking it seriously now is the best way of avoiding a more extended acquaintance in the near future.