Sad, but true.
Adding to this - for what you aim to get from status (lounge access while flying economy, airport benefits) you generally will need to qualify for the mid-tier level, which in most programs kicks in at 50,000 flown miles/50 segments. Also, most airlines have made it more difficult for passengers on deep discount economy fares to qualify for status, be it through outright spend requirements (AA) or through a tier point system (BA, QR...) that disproportionately rewards premium cabin travel and disadvantages those in the cheapest fare classes.
With only 20k miles flown annually on deep discount shorthaul flights within Europe, forget about status. Buy a Priority Pass membership (or get a credit card that comes with PP) for lounge access. Even though this is FT, flying an extra 30k miles and spending four figures on mileage runs just to get status is not something I`d recommend in your case.

Continue to bank your miles with AA or check out the IAG airlines (BA, IB, maybe Aer Lingus' new program) as in all other programs your miles will expire before you have collected enough for redemptions, especially if your aim is longhaul premium class awards and/or multiple awards for family travel. Also, look into co-branded credit cards for non-flying points accrual (some programs even award status miles for cc spend, like AB topbonus German and Austrian cards, or the higher-tier US airline cards on offer for US residents).