No, for the bearing (or ANY bearing) to work properly, the axle must be supported with a tight fit. Otherwise it will flex, possibly leading to fatigue and failure (snapping under load).
You need to replace 2 items
1- the bearing (and possibly it's mate on the other side
2- the mechanic who considered this OK.
BTW- it's possible that the bearing is correct, but a shim of some kind was omitted (I don't stay up with every BB or crankset), but the effect is the same. Also check the other side, since riding this way would have stressed the other bearing causing excess load and wear.
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