Most online airport-transfer brands you'll find for Stuttgart are aggregators — they take your booking, mark it up, and forward it to whichever driver accepts the lowest payout, with no licensed taxi company standing behind the ride.
Every ride is performed by a PBefG-licensed taxi company (§ 47 Personenbeförderungsgesetz), with drivers of those companies and vehicles from the Mercedes E-Class, V-Class and S-Class range. You book, pay and get your invoice from one contract partner. The managing director is a board member of the Stuttgarter Taxi-Verband (STV) — the regional association that represents the licensed taxi trade.
For your travel managers, that means three things in practice: one contract partner to invoice, one contact to escalate to, one party that's accountable if the service falls short.