ATC DID NOT ASSURE ARPT WAS CLR OF OBSTRUCTIONS ON RWYS AND TXWYS WHEN THEY WERE RPTED BY ACFT AFTER A PASSING TSTM.

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EXTENDED TAXI TIME (2 HRS 52 MINS) DUE TO GND STOP TO DEST (LGA) AND TSTMS AT CLT. ARPT WAS CLOSED FOR OVER 30 MINS DUE TSTMS; WINDS OVER 45 KTS; LIGHTNING STRIKES ON ARPT; ETC. RAMP AREA CLOSED. DURING TAXI TO RWY 36R; OTHER ACFT RPTED DEBRIS (BAGGAGE CART; PROPANE TANK; OBSTRUCTION BARREL) ON/NEAR TXWYS/RWYS TO ATC. ATC DID NOT ADVISE OTHER ACFT. ATC CONTINUED TAXI/DEP/ARR OPS. NO RWY INSPECTION WAS MADE PRIOR TO RECOMMENCING OPS ON RWYS/TXWYS. WHAT WENT RIGHT? WHY? COMPANY ACFT ADVISED ATC OF DEBRIS SIT. WHAT WENT WRONG? WHY? ARPT DID NOT CONDUCT FAR PART 139 REQUIRED FIELD INSPECTION PRIOR TO REOPENING ARPT. ATC CONTINUED OPS WITHOUT DETERMINING IF ARPT WAS CLR OF DEBRIS AND UNDAMAGED. ATC DID NOT ADVISE ACFT THAT THIS WAS NOT DONE. WHAT WAS LEARNED? (DESCRIBE): CREW FATIGUE! WE CAN ONLY WORK WITH THAT INFO WHICH WE ARE ADVISED OF. WHAT WOULD YOU DO DIFFERENTLY IF FACED WITH THIS OR A SIMILAR SIT AGAIN? CHALLENGE ATC FOR THE INFO AND DELAY IF NECESSARY. WHAT NEEDS TO BE ADDRESSED TO PREVENT A RECURRENCE OF THIS SIT AND IMPROVE SAFETY? ATC/ARPT NEED TO COORDINATE AND COMMUNICATE. ATC NEEDS TO ADVISE ACR CREWS OF THE SIT. ARPT NEEDS TO FULFILL ITS DUTIES TO ENSURE AIRFIELD IS SAFE PRIOR TO REOPENING.