Why can't ligands with "locked structures" undergo chelation?
My copy of Concise Inorganic Chemistry, 5th edition (J.D.Lee, Wiley publishers)1 has nothing contrary to say about hydrazine or 1,4-diazabicyclo[2.2. 2]octane (henceforth referred to as DABCO). It is most likely that the author of your adaptation has used his liberty to add these facts in your copy.
This then raises the question: is the author correct? Hydrazine derivatives such as Benzhydrazides and Salicylhydrazides 2 have been proven to show chelation. Pure hydrazine, however, is unlikely to show chelation due to excessive ring strain. Also, no literature has been found which shows hydrazine undergoing chelation. DABCO, on the other hand, forms complexes with Mercury halides3 with a denticity of 1. This ligand also does not show chelation, and fitting a large metal atom even off-center is highly unlikely due to large steric hindrance and the geometry of the lone pair, which is perpendicular to the structure and not favourable for chelation. Most complexes formed by DABCO tend to be linear in nature4 and no rings are formed.
In short, the author is correct in stating that hydrazine and DABCO do not form chelates.
EDIT: You may also want to read more on a class of compounds called Cryptands, specifically Cryptand-222. This compound displays the 'cagelike' ligation you were looking for in DABCO.
References:

Lee, J. D. Concise Inorganic Chemistry. 5th ed, Wiley publishers &amp;
Blackwell Science, 1996.
Issa, R. M., et al. Coordination compounds of hydrazine derivatives
with transition metals. I. Metal Chelates with Benzhydrazide and
Salicylhydrazide. Zeitschrift fur anorganische und allgemeine
Chemie, vol. 354, no. 1–2, Sept. 1967, pp. 90–97.
doi:10.1002/zaac.19673540118.
Shan, Zeng-Mei, et al. Synthesis, Crystal Structures, and
Characterization of Three Mercury(II) Halides Inorganic–Organic
Hybrid Compounds with 1,4-Diazabicyclo[2.2.2]Octane Ligand.
Inorganica Chimica Acta, vol. 366, no. 1, Jan. 2011, pp. 141–46.
doi:10.1016/j.ica.2010.10.023.
Thorp-Greenwood, Flora L., et al. Three-Dimensional Silver-Dabco
Coordination Polymers with Zeolitic or Three-Connected Topology.
Crystal Growth &amp; Design, vol. 14, no. 11, Nov. 2014, pp. 5361–65.
doi:10.1021/cg501231v.