Oracle 21c

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.

OBJECTID	ASSET_ID	DATE_
1	1	01-APR-16
2	1	01-MAR-19
3	1	01-JAN-22
4	2	01-APR-16
5	2	01-JAN-21
6	3	01-MAR-22
7	3	01-APR-16
8	3	01-MAR-18
9	3	01-MAR-13
10	3	01-JUN-10

--Select the greatest n per group: For a given ASSET_ID, select the inspection that has the latest DATE_. 
--Ignore from here...
with road_insp (objectid, asset_id, date_) as (
select  1, 1, to_date('2016-04-01','YYYY-MM-DD') from dual union all
select  2, 1, to_date('2019-03-01','YYYY-MM-DD') from dual union all
select  3, 1, to_date('2022-01-01','YYYY-MM-DD') from dual union all
select  4, 2, to_date('2016-04-01','YYYY-MM-DD') from dual union all
select  5, 2, to_date('2021-01-01','YYYY-MM-DD') from dual union all
select  6, 3, to_date('2022-03-01','YYYY-MM-DD') from dual union all
select  7, 3, to_date('2016-04-01','YYYY-MM-DD') from dual union all
select  8, 3, to_date('2018-03-01','YYYY-MM-DD') from dual union all
select  9, 3, to_date('2013-03-01','YYYY-MM-DD') from dual union all
select 10, 3, to_date('2010-06-01','YYYY-MM-DD') from dual
) SELECT * FROM road_insp WHERE
--...to here

--SQL expression:
NOT EXISTS (
        SELECT *
        FROM road_insp r2
        WHERE r2.asset_id = road_insp.asset_id AND r2.date_ > road_insp.date_
       )

ORDER BY asset_id

OBJECTID	ASSET_ID	DATE_
3	1	01-JAN-22
5	2	01-JAN-21
6	3	01-MAR-22